Brainteaser - Tie During a Random Vote Count

A ballot box contains 400 slips: 100 for Party A and 300 for Party B. The slips are thoroughly mixed, then counted one-by-one in random order. Let \(A_t\) and \(B_t\) be the cumulative counts after \(t\ge 1\) slips have been drawn. What is the probability that at some point during counting (after counting has started), the running totals tie, i.e., \(A_t=B_t\) for at least one \(t\ge 1\)?