Chess Tournament VI

In a chess tournament with 50 players numbered from 1 to 50, a series of 49 matches determines the winner. The tournament begins with two randomly selected players competing in the first match. In each subsequent match, the loser is eliminated, and the winner plays against another randomly selected player who has not yet been eliminated. Suppose that the player with the larger number always defeats the player with the smaller number. What is the probability that player 49 and player 50 play the final match?

Enter your answer rounded to 5 decimal places.