Why was India partitioned into three countries at the end of World War 2?

Answer 1

It was not.

At the end of the war India was still one country. India was partitioned into TWO countries India and Pakistan when the people of the former British colony obtained their Independence from Britian. The Muslim people in the colony insisted on the separation as part of the independence agreement.

However, the country of Pakistan could not hold itself together politically and ssome time later broke into two independent countries, one on each side of modern India.

Answer 2

Because as the British negotiated to give Imperial India back to its peoples, the Muslim leader Muhammad Ali Jinnah insisted on and demanded the formation of independent states in the East and the West of British India for the Muslims - these became a new country "Pakistan".

Much later these to Muslim states decided they would go their own ways, resulting in 3 countries as a result of independence.