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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