Using the Bayes’ approach, let’s break up the world into Hearts (H) and non-Hearts (N). Easily,
\begin{equation*}
P(A|H) = 1/13
\end{equation*}
\begin{equation*}
P(A|N) = 3/39
\end{equation*}
and so by Bayes’
\begin{equation*}
P(H|A) = \frac{P(H) P(A|H)}{P(H) P(A|H) + P(N) P(A|N)}
= \frac{\frac{13}{52} \cdot \frac{1}{13}}{\frac{13}{52} \cdot \frac{1}{13} + \frac{39}{52} \cdot \frac{3}{39}} = \frac{1}{4}
\end{equation*}
as expected!