Please solve the programming task below using a self-contained code snippet in a markdown code block.

n passengers board an airplane with exactly n seats. The first passenger has lost the ticket and picks a seat randomly. But after that, the rest of the passengers will:

Take their own seat if it is still available, and
Pick other seats randomly when they find their seat occupied

Return the probability that the nth person gets his own seat.
 
Please complete the following python code precisely:
```python
class Solution:
    def nthPersonGetsNthSeat(self, n: int) -> float:
```