We are given $P(A \cap B) = \frac{1}{8}$ and $P(\bar{A}) = \frac{3}{4}$. We need to find $P(\frac{B}{A})$.

First, we find $P(A)$ using the complement rule: $P(A) = 1 - P(\bar{A}) = 1 - \frac{3}{4} = \frac{1}{4}$.

Next, we use the formula for conditional probability: $P(\frac{B}{A}) = \frac{P(A \cap B)}{P(A)}$.

Substituting the given values, we get $P(\frac{B}{A}) = \frac{\frac{1}{8}}{\frac{1}{4}} = \frac{1}{8} \times \frac{4}{1} = \frac{4}{8} = \frac{1}{2}$.