So how did the SL army transform from a running army to a winning army in the final war?

Short Answer

The army adopted a different strategy that exploited the Tigers' principal weaknesses while neutralizing their strengths. In simple terms, the Army fought like Tigers, while the Tigers were forced to fight like the army.

Long Answer

1. Army Deep Penetration Unit (LRRP) - One of the reasons the Tigers were incredibly successful is because of their ability to penetrate deep into army-controlled territories undetected and mount surprise attacks on political, military, and economic targets anywhere in Sri Lanka. Because of this, the Sri Lankan army couldn't use its massive numerical advantage to crush the Tigers, as they also had to deploy most of their troops across Sri Lanka to maintain internal security, while the Tigers could use their entire force to mount and defend attacks. The army carefully studied this weakness and Tiger strategies, creating its own Deep Penetration Unit modelled after Tiger units. LRRP personnel received specialized training in Sri Lanka and abroad. LRRP teams also received support from disgruntled ex-Tigers and members of anti-Tiger Tamil militant groups. Hence, LRRP units were successful in assassinating several high-level commanders of the Tigers in Tiger-held territory. The first successful attack was against Colonel Shankar, the head of the tiger air wing, killed by a claymore mine set up by LRRP. This made the Tigers not commit their entire force to fight,  forcing them to redeploy some 5,000 fighters in force protection duties to guard its lines of communication and supply. Due to this loss of manpower, in the final war, the army had the edge because of their numerical advantage.

2. Small Unit Tactics - Another reason the Tigers were incredibly successful is because of their expertise in Small Unit Tactics. This involves using soldiers in small teams to conduct warfare instead of committing entire army divisions. The ability to employ small infantry units allows them to infiltrate army lines on a wider front. Consequently, the army's numerical superiority is nullified, as they are compelled to spread out their troops to engage in a wider front. This tiger strategy also neutralizes another advantage of the army, which is their superior artillery and air force. These are more effective against large groups than spread-out small teams. As a result, the army's airforce and artillery advantages become ineffective. Simultaneously, the Sri Lankan army committed entire divisions to fight, and Tiger artillery teams, including artillery observers, were highly capable cadres. They pounded the army divisions with pinpoint accuracy, inflicting heavy casualties. It is estimated that casualties caused by Tiger artillery and mortars before the final war were as high as 60% of total casualties. Most soldiers were killed even before getting close enough to engage the Tigers.

Learning from its mistakes, the army revised its land warfare doctrine to strongly emphasize small unit section-level operations, mirroring the Tigers' tactics. In the final war, the Army Special Forces and the Commandos changed the battlefield dynamic by deploying small four-man teams. So just like the army in previous wars, the Tigers were now forced to fight on a wider front and highly skilled tiger artillery teams were rendered useless. In the final war, infantry casualties caused by Tiger artillery and mortar fire were reduced to only about 35%. So most battles were decided by close-range combat, where the army's numerical superiority gave them an incredible edge.

3. Karuna Amman's defection - On 26 July 2004,  Colonel Karuna Amman broke away from the Tigers. Karuna was a formidable field commander who won many decisive battles in the north and east for the Tigers. With Karuna's defection, the Tigers lost an expert field commander, and nearly 6000 loyal Tigers from the eastern province, especially from the Jeyanthan Regiment. The Jeyanthan Regiment, an elite infantry formation, was founded and trained under Karuna's leadership, making it the second oldest and most feared infantry unit of the Tigers. It is said that the army feared the Jeyanthan Brigade the most and actively sought to avoid direct clashes with them. The Jeyanthan Brigade never recovered from the split, as many defectors joined Karuna's paramilitary faction and fought alongside the Sri Lankan army during the Eastern Theater of the final war. As a senior and highly trusted commander, Karuna possessed intricate knowledge of Tiger battle strategy, safe houses, bunkers, and ammunition depots. Therefore, it allegedly provided the army with crucial intelligence, offering deep insights into the Tigers as a fighting organization before entering the final war. This caused the Tigers to fight with most of their military secrets exposed.

4. 2004 Tsunami - The Tigers redeployed a huge number of cadres and senior commanders, including their star commander Brigadier Balraj, from Vanni heartland to the East after Karuna's defection to monitor and control Karuna and his group. This redeployment coincided with the 2004 Tsunami. Over two-thirds of the tsunami damage in Sri Lanka was concentrated in the North and East, which were under Tiger control. So sea Tiger assets were badly damaged, and Tiger cadres suffered heavy casualties. Even Brigadier Balraj narrowly escaped when the tsunami struck his camp at Vaharai in the Batticaloa district. This once again reduced tiger fighting capabilities before entering the final war.

5. High recruitment drive- The principal weakness of the Tigers lies in their finite manpower base. Only 12 per cent of Sri Lanka's population were Lankan Tamils, and among them, only around 300,000 Tamils resided in areas directly controlled by the Tigers after the loss of the Jaffna district in 1995, which had a Tamil population of 600,000 people, and following the decline in recruitment in the Eastern province due to Karuna's influence. Consequently, the Tigers had only a limited pool from which to recruit fighters, explaining their desperation to recapture Jaffna even before Karuna's defection. If not for Indian assistance, they might have retaken Jaffna in 2000. After the victory in the second Battle for Elephant Pass in 2000, the Tigers continued their advance, successfully capturing Chavakachcheri town near Jaffna municipal limits, thereby threatening to retake Jaffna with over 40,000 Sri Lankan soldiers trapped inside. Through Indian Defence Minister George Fernandez, the Indian government pressured the Tigers to halt their Northern push, providing the breathing space the Army desperately needed. If the Tigers had captured Jaffna, it would have made it very difficult to defeat them militarily in the final war. Furthermore, the Tigers were never interested in recruiting Tamils from India. Had they considered it, with over 80 million Tamils in India, it would have made it nearly impossible to defeat the Tigers. Therefore, the tigers with shrinking manpower couldn’t sustain the fight. 

On the other hand, before 2005, the Army faced difficulty recruiting even 3,000 soldiers per year. The newly sworn-in Mahinda government increased the armed forces budget by 40%, securing a $1 billion loan from China, with additional financial assistance, including lines of credit for oil and arms purchases, provided by Iran, Libya, Russia, and Pakistan. The increased budgets allowed the army to recruit more personnel. By late 2008, the Army was recruiting 3,000 soldiers a month. From approximately 120,000 personnel in 2005, the army grew to more than 200,000 by 2009, making it the 14th largest military in the world.

6. Help of foreign militaries - The capability of Sri Lankan Air Force (SLAF) pilots for night operations has been reported as poor, leading to allegations that many air strikes by the SLAF were carried out by mercenary Ukrainian and Russian pilots. The crash of the MiG 27, piloted by Ukrainian Captain L. Veralli, was attributed to 'language difficulties' between Sri Lankan and foreign pilots. Additionally, a Mi-24 gunship, shot down by the LTTE, was reportedly flown by two Russian mercenaries. Pakistani counter-insurgency experts and Air Force officers also allegedly assisted the offensive. On August 14, 2006, a convoy carrying the Pakistani High Commissioner to Sri Lanka was attacked by the Tigers, in an attempt to compel Pakistan to cease its support for Sri Lanka.

To enhance Sri Lanka's capabilities, the Indian Air Force provided the sophisticated "Indra II" radar system to identify Tiger aircraft, and stationing personnel to operate them. During a combined Tiger air and land raid on the Vavuniya Airbase, two Indian Air Force officers serving there were wounded. Extensive satellite imagery provided by India also aided Sri Lanka in identifying Tiger positions in densely wooded areas. America assisted by disrupting tiger offshore military equipment procurement, providing a Coast Guard vessel, and supplying an important national naval command and control system. Given Sri Lanka's island geography, the Tigers depended on the sea for arms imports. However, American and Indian intelligence pinpointed the locations of Tiger boats transporting weapons. This information enabled the Sri Lankan Navy to hunt down and destroy these boats, often several thousand kilometres off Sri Lankan territorial waters. These activities successfully choked off Tiger arms imports during the final war. 

So, the Tigers faced not only the military might of the Sri Lankan Army but also the combined pressure and interventions of multiple countries during the final stages of the conflict, which was impossible to handle even for a fighting force of their calibre. Thus, the Tigers, the only non-state armed force in the world to have a formidable navy and airforce, along with their own homemade submarines and battle tanks, and an army thought to be invincible even by Western military advisors, came to an end. 

Summary

While numerous uncontrollable factors worked against the Tigers, it is essential to acknowledge that triumph ultimately favoured the side with the most effective strategies, even though it took the government over 26 years to discover them. The government demonstrated the ability to adapt its strategies in the face of persistent setbacks and emerged victorious. In contrast, the Tigers tenaciously adhered to their previously successful formula, resulting in their defeat.

Future

The tiger's innovative skills and military achievements within 26 years are examples of the tremendous potential that Tamils are capable of. Even after 14 years since the end of the war, Sri Lanka has failed to find a political solution and continues to neglect tapping into those skills for constructive purposes. As they say, an idle mind is the devil's workshop. Unlike what many of you believe, the peace we've achieved is just temporary. As a fervent student of history, I know that peace is never won on the battlefield but at the negotiation table. We have achieved victory in a war, but not yet in establishing lasting peace.