# Geometric Probability

Let $$a$$ and $$b$$ be real numbers. Let $$P$$ denote probability that the absolute difference between $$a$$ and $$b$$ will is greater than their average. If the value of $$P$$ is in the form of $$\frac xy$$ for coprime positive integers $$x$$ and $$y$$, find the value of $$x+y$$.

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