||Deterministic evolutionary dynamics can lead to stable coexistences of different types. Stochasticity, however, drives the loss of such coexistences. We investigate the most probable extinction trajectory by mapping a stochastic evolutionary model to a problem of classical mechanics using the Wentzel-Kramers-Brillouin (WKB) approximation. We consider competitive Lotka-Volterra type dynamics with coexisting two species. Our results show that more abundant types in a coexistence are not always likely to go extinct first. Instead, the distance between the coexistence and extinction point is a better predictor of extinction.