Airplane seating probability

An airplane has 300 seats, and you are last in line out of 300 passengers with boarding passes. The 1st boarding pass holder is crazy , and chooses the seat randomly (the probability of choosing each free seat is the same). Every passenger in line takes the next seat, according to their boarding pass if it is available, otherwise, the passenger takes an available seat randomly.

If the probability of choosing each free seat is the same, what is the PERCENTAGE probability that you take the seat designated to you in your boarding pass?

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