A rectangle $ABCD$ has side lengths $AB=6 \, \text{miles}$ and $BC=9\, \text{miles}$. A pigeon hovers at point $P$, which is 5 miles above some randomly chosen point inside $ABCD$. Given that the expected value of $AP^2 + CP^2 - BP^2 - DP^2$ can be expressed as $\frac{a}{b}$, what is $ab$?

Let's think step by step and output the final answer within \boxed{}.
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