International Mathematical Olympiad 1998 Problem 2

In a competition, there are $a$ contestants and $b$ judges, where $b \geq 3$ is an odd integer. Each judge rates each contestant as either "pass" or "fail". Suppose $k$ is a number such that, for any two judges, their ratings coincide for at most $k$ contestants. Prove that $k/a \geq (b - 1)/(2b)$.