Its 50%

Two possible outcomes
Outcome 1: Mr Ford takes someone's seat who takes someone else's seat etc. until somewhere along the line, someone takes Mr. Ford's seat.

Outcome 2: Mr Ford takes someone's seat who takes someone else's seat etc. until somewhere along the line, someone takes your seat.

As soon as one of the two outcomes is met, the loop closes. The loop has a 50% chance of closing with the last person.

The Loop goes from Mr Ford takes person A's seat. Until we get to person A, everyone else takes their assigned seat. Then person A takes either your seat, Mr Ford's seat, or person B's seat. Until we get to person B, everyone else takes their assigned seat. Then person B takes either your seat, Mr Ford's seat, or person C's seat. We can go through as many people as we need to, but regardless of how many people we go through, the chances of it ending when someone takes Mr. Ford's seat are equal to the chances of it ending when someone takes your set.