ブラウン運動と達成する時

最近リスクラッテのクイズを受けながら悩んでいます。The problem is that, given a current position of y0, a position a to its left, and a position b to its right, find the probability that the particle reaches a before it reaches b. This seems to involve the probability that a "net left" of y0-a precedes a "net right" of b-y0.
The RiskLatte answer of (y0-a)/(b-a) seems difficult to justify. The probability seems to translate to:
P(xs=-a)*integral(t from 0 to s)(P(xt