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Probability Level 4

Suppose Finn and Sharky are playing a match of games in which they have respective probabilities of $\dfrac{4}{7}$ and $\dfrac{3}{7}$ of winning any single game, (no ties are possible).

The match ends when one of the players wins two consecutive games. The probability that Finn wins the match is $\dfrac{a}{b}$ , where $a$ and $b$ are positive coprime integers.

Find $b - a$ .