Why are there no tigers in Sri Lanka?

Sri Lanka has no tigers because the island was separated geologically from the Indian mainland a long way back before tigers even started migrating southwards through the Indian subcontinent, in general.

Rising sea levels formed the Palk Strait thousands of years ago, and in a real sense, it left Sri Lanka isolated, which helped keep a singular, local ecosystem intact. Because the Sri Lankan leopard (Panthera pardus kotiya) evolved inside this closed setting, with no natural pressure or larger predators around like tigers or lions, it became the island’s top hunter, really unquestioned. Over time, it grew notably larger than its mainland relatives.