Exponential distribution to represent crash game

I'm sure many of you have heard of the game called crash. Some popular examples of this are satoshi, bustabit.

It's pretty complicated to explain, so I will begin assuming that you are familiar with it.

Anyways, my goal is to recreate something along these lines. I want to make a function that will give me an exponential distribution double PRNG between 1 and 100.

Basically, a random double between 1 and 100 in which the probability of getting a double near 1 is much more likely than getting a double closer to 100.

I've been experimenting with a few things so far, but I really just can't figure this one out. Any insight as to how this could be achieved would be greatly appreciated.