How to Tell How Likely a Signal Is Present in Another One (Variance Unknown)?
Though the Matched Filter is the best tool detection of a known signals under AWGN it should work well here as well.

To say something about the probabilities the question is, do you know something about the energy of the received signals?
If you do, you should easily say something about the probabilities.  

Pay attention that if the assumption is a signal could be within a different signal you need to apply a generalized Matched Filter (Multi Decision).