Will the Scoreboard Ever Be Level?

A chess club elects its president. Candidate X received 100 ballots and candidate Y received 300, all 400 sitting shuffled together in a box. The secretary pulls ballots out one at a time, in uniformly random order, updating a running scoreboard after each one. What is the probability that at some moment during the count — after at least one ballot has been read — the two candidates' running totals are equal?