We have a biased 1-dimensional random walk on the number line. Each timestep, with probability $p$ such that $0<p<1$, it increments by $1$, otherwise it decrements by $1$. Given positive integers $a$ and $b$, we want to know the probability of hitting $-a$ before hitting $b$ (when starting at $0$).
From https://en.wikipedia.org/wiki/Random_walk#One-dimensional_random_walk, I know that the result for unbiased random walks (i.e. $p=\frac{1}{2}$) is $\frac{b}{a+b}$. But how to derive for biased random walks?