Probabilistic Parking Spaces

A row of street parking has spaces numbered 1 through 100, in that order. Each person trying to park drives by the spaces one-by-one starting at number 1.

At each open space, they are told how many open spaces, \(S,\) they haven't passed (including the current space). They park in that space with probability \(\frac{1}{S};\) otherwise, they move on to the next open space.

What is the expected value for the parking spot of the \(100^\text{th}\) person to arrive (assuming no one has left and only one car goes through the parking process at a time)?

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