I think it starts at 100%, so (100!)/(100^100) but that is the same as (99!)/(100^99) lol.
Edit: has anyone considered whether the 1% increase is actually 1% of the new probability instead of the original? For example, 100%, 99%, 98.01% etc. instead of 100%, 99%, 98% etc. In this case the formula would be 0.99^(99) = 0.36972963765, but this is surely not true.
So (100!)/(100^100), I think.