Chess Tournament

A chess tournament has $2^n$ players ranked by skill from $1$ (best) to $2^n$ (worst). The tournament is a single-elimination (knockout) format: after each round, only the winner advances to the next round. In each round, the remaining players are paired at random. Whenever two players meet, the higher-skilled player always wins.

Question : What is the probability that players 1 and 2 meet in the final?