Given: \(P(A/B) = P(B/A)\) and \(P(A/B) \ne 0\)

We know that \(P(A/B) = \frac{P(A \cap B)}{P(B)}\) and \(P(B/A) = \frac{P(A \cap B)}{P(A)}\)

Since \(P(A/B) = P(B/A)\), we have \(\frac{P(A \cap B)}{P(B)} = \frac{P(A \cap B)}{P(A)}\)

Since \(P(A/B) \ne 0\), it implies that \(P(A \cap B) \ne 0\). Therefore, we can safely divide both sides by \(P(A \cap B)\)

So, \(\frac{1}{P(B)} = \frac{1}{P(A)}\), which implies \(P(A) = P(B)\)