I know that we need some sort of sensitivity(global, local) to calculate noise that needs to be added for differential privacy. The noise is the maximum difference between two neighboring datasets. However, if I am working in probability spaces, i.e. my values are bounded by 0,1. My sensitivity would be 1, which seems too large for adding noise to the probabilities.
I tried looking up any relevant literature that provides any tighter upper bounds, but no success. I am only interested in adding noise to the probabilities, not to the mechanism that they are generated from.