numpy irreversibly change items in a list at random

I have a list

a = np.ones(1,size=100)

I want to turn 50 random items in that list to 0. Once those elements are 0, I want to turn 25 random elements of the remaining items in the list to 0. Of the remaining 25 ones, I want to turn 13 of the remaining elements to zero at random etc.

This is basically to simulate exponential decay, but I'm struggling to think of an algorithm to do this.