For solving a related probability problem, I need to solve the following recurrence relation:-

$q(r,b,L)=\frac{b}{r+b}q(r,b-1,L)+\sum_{k=1}^{L}\frac{r}{r+b}\times\cdots \times \frac{r-(k-1)}{r+b-(k-1)}\times\frac{b}{r+b-k}q(r-k,b-1,L)$

where $r, b$ and $L$ are positive integers with the following conditions: $q(r,b,L) = 1$ whenever $r \leq L$ and $q(r,0,L) = 0$.

How do I solve this recurrence relation?