Dice rolling mechanic where modifiers have a predictable and consistent effect on difficulty

I am looking for a dice rolling mechanic that makes it such that increasing or decreasing a modifier on the roll has a constant multiplier effect on the probability of the outcome.

Say you have to make a roll for STAT. Such a roll has a probability of success of 50%. Now say you roll with a mod of -1, this roll has a probability of success of 25%. -2 has a probability of 12.5%. -3 is 6.25% and so on, always halving. The other way around it should be the same but for the probability of failure, always being divided by the same factor.

It doesn’t have to be a multiplier of 0.5, in fact I’d much rather it was a multiplier of 0.66-0.75, not such an extreme change. The default unmodded value doesn’t need to be 50% chance of success either, it can be something else.

Is there any kind of dice rolling mechanic I can use to simulate something like this?