Gambler's Ruin with State-Dependent Win Probability

A gambler's fortune evolves on $\{0, 1, 2, 3, 4\}$ with absorbing barriers at $0$ and $4$. At state $k$ ($1 \le k \le 3$), she wins $\$1$ with probability $p_k = \frac{k}{2k+1}$ and loses $\$1$ with probability $q_k = \frac{k+1}{2k+1}$. Starting from state $2$, find the probability of ruin (absorption at $0$).