Don't shoot the animal, hunter!

A sportsman's chance of shooting an animal at a distance \(R(>A)\) is \(\frac{A^{2}}{R^{2}}.\) He fires when \(R=2A\) and if he misses, he reloads and fires when \(R=3A,4A,5A\cdots\) and so on. If he misses at distance \(1729A,\) the animals escapes.

If the probability that the animal escapes is \(\frac{a}{b}\) where \(a\) and \(b\) are coprime integers, what is the value of \(b-a?\)

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