This paper contains two main results: First, we revisit the well-known visibility based pursuit-evasion problem and show that, in contrast to deterministic strategies, a single pursuer can locate an unpredictable evader in any simply-connected polygonal environment using a randomized strategy. The evader can be arbitrarily faster than the pursuer and it may know the position of the pursuer at all times but it does not have prior knowledge of the random decisions made by the pursuer. Second, using the randomized algorithm together with the solution of a known lion and man problem [1] as subroutines, we present a strategy for two pursuers (one of which is at least as fast as the evader) to quickly capture an evader in a simply-connected polygonal environment. We show how this strategy can be extended to obtain a strategy for (i) capturing the evader in a polygonal room with a door, (ii) two pursuers who have only line-of-sight communication, and (iii) a single pursuer (at the expense of increased capture time).