Chess Tournament

A chess tournament has $K$ levels and $N = 2^K$ players with skills $P_1 > P_2 > ... >P_{N}$. At each level, random pairs are formed and one person from each pair proceeds to the next level. When two opponents play, the one with the better skills always wins. What is the probability that players $P_1$ and $P_2$ will meet in the final level?