Problem 8

On a sunny beach of Mathstopia, there are 2023 tents in a row, numbered 1 through 2023, to provide shelter from the blazing sun. The beach is popular, so they fill up quickly. The first person to arrive chooses a tent randomly. Those arriving later will randomly choose a tent that has maximal distance from the tents already occupied. What is the probability that tent number 1 is occupied last? Give your answer as a decimal rounded to 10 decimal places.