For two events A and B ait is given that $P(A)= P(A/B)=\frac{1}{4}$ and $ P(B/A)=\frac{1}{2}$. Then,

A and B are independent events such that $P(\overline{A}/B)=3/4$

We have,

$P(A)=P(A/B)=1/4$

This shows that A and B are independent events.

∴ $P(B) = P(B/A)= 1/2$

Now, $ P(A/B)=\frac{1}{4}⇒ P(\overline{A}/B)=1-\frac{1}{4}=\frac{3}{4}$