計算機數學

The following questions constitute a set. Please answer accordingly.

Suppose $A$ and $B$ are events in a sample space, such that $P(A) = \frac{4}{9}$, $P(B) = \frac{5}{11}$, $P(A|B) = \frac{2}{5}$, and $P(B|A) = \frac{a}{b}$ (where $\frac{a}{b}$ is an irreducible fraction).

(4分) $a = ?$