There are mathematical formalisms (like possibility theory http://scholarpedia.org/article/Possibility_theory http://scholarpedia.org/article/Possibility_theory

There are mathematical formalisms (like possibility theory http://scholarpedia.org/article/Possibility_theory http://scholarpedia.org/article/Possibility_theory - this article seems to be better than in Wikipedia) that allow making decisions based on the relative likelihood of events (those "degrees of surprise"). It can be useful when the actual probabilities of events are not known (it's often the case in real life scenarios). Then possibility theory may actually tell you what decision to make based on this limited information. My understanding is that the point is not that probability theory does not work, but that it requires a lot of knowledge about the system, which might be not available to the agent. In such situations, possibility theory provides a framework for making reasonable deductions.