A Puzzle By Midnight Math

Kevin buys a bus ticket from Singapore to Malaysia, but he is unaware that his ticket has an assigned seat. Upon boarding the bus, he sits in a random empty seat. Passengers continue to board and sit in their assigned seats until a passenger sees Kevin in their seat. The passenger, not wanting to be rude and displace Kevin, assumes they have made a mistake and sits in a random empty seat. The next passenger whose seat was taken also sits in a random seat, and so on until the last passenger sits in the last seat left. Given that the order of passengers entering (including Kevin) is random, and that each passenger (who isn’t Kevin) will sit in their assigned seat unless it’s taken, and that Kevin is not the last passenger, what is the probability that the last passenger in line will sit in their assigned seat?

Send in your solutions (with proofs) to midnight.math@outlook.com. If you are correct, you will be given the highest of accolades: your name mentioned here, next issue.