Random Walk: Hitting Probability

A particle starts at position 0 on the integer line. At each step, it moves +1 or −1 with equal probability $1/2$, independently of past steps. The walk stops when the particle first reaches either $\alpha$ (where $\alpha > 0$) or $-\beta$ (where $\beta > 0$).

Question: What is the probability that the walk stops at $\alpha$?