Triangle \(ABC\) has side lengths \( BC = 13, CA = 14, AB = 15\). A point \(P\) is selected at random from the interior of the triangle and the line \(AP\) is extended to meet \(BC\) at the point \(Q\). What is the expected value of \([ABQ]\)?
Details and assumptions
\([PQRS]\) denotes the area of figure \(PQRS\).