audio - Determining the probability of two signals, with added independent noise, being the same?

I have the first 100ms of two signals, each with a noise independent to that signal. I want to compare the two signals and determine the probability that these two signals are (minus noise) the same, and therefore come from the same source, i.e. if whether they are unique or not.

I am hoping there is a standard approach to a problem of this sort, and any hint in the right direction would be greatly appreciated. I did have a hacky machine learning approach, involving feature extraction and Euclidean space, but being a signal novice, I thought I'd ask here first.