Seeded Into Halves

32 teams are drawn uniformly at random into the 32 slots of a single-elimination bracket. Slots 1 to 16 form the top half and slots 17 to 32 the bottom half, so the winner of each half plays the final: two teams meet in the final exactly when they sit in different halves and each wins its own half.

Teams are numbered by strength and the stronger number always wins. Team #1 beats everyone, Team #2 beats everyone except #1, and so on.

What is the probability that the final is Team #1 against Team #3?

Answer format: round to 3 decimal places.