By definition of \(P(A|B)\):
\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \]
If \(P(A|B) = P(A)\):
\[ P(A) = \frac{P(A \cap B)}{P(B)} \]
Rearranging the above:
\[ P(B) = \frac{P(A \cap B)}{P(A)} \]
Since \(\frac{P(A \cap B)}{P(A)} = P(B|A)\):
\[ P(B) = \frac{P(A \cap B)}{P(A)} \implies P(B) = P(B|A) \]