A Hat Trick
There are 100 people in a room, all of them wearing different hats. Everybody puts their hat in a large basket.
Later, after thoroughly shuffling the hats, each person takes out one hat and wears it.
Let the probability of a randomly picked person wearing their own hat be \(x\%\).
What is \(\left[1000x\right]\), where \([x]\) denotes the greatest integer less than or equal to \(x\).