condition exponentially less likely per loop pass

I want to achieve a condition inside a for loop, which will get exponentially less likely to be true after every loop pass.

Here is a simplified version of my current, linear solution: every loop pass it is x+1 less likely that the random number === 0 and thus the probability per run is reduced.

for (let x = 0; x < 10; x++) {
    if (getRandomInt(0,x) === 0) {
        // do something
    }   
}

function getRandomInt(min, max) {
    min = Math.ceil(min);
    max = Math.floor(max);
    return Math.floor(Math.random() * (max - min + 1)) + min;
}

But I don't know how to change the condition so that the probability per loop pass becomes exponential and not linearly smaller as in my solution.

Anyone an idea? Thanks for your time!