Eight players \( \mathrm{P}_{1}, \mathrm{P}_{2}, \mathrm{P}_{3}, \ldots \ldots \ldots \mathrm{P}...

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Eight players \( \mathrm{P}_{1}, \mathrm{P}_{2}, \mathrm{P}_{3}, \ldots \ldots \ldots \mathrm{P}_{8} \) play a knock out tournament. It is known that whenever the players \( P_{i} \) and \( P_{j} \) play, the player \( P_{i} \) will win if \( ij \). Assuming that the players are paired at
\( \mathrm{P} \) random in each round, what is the probability that the players \( \mathrm{P}_{4} \) reaches the final ?

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