billswift comments on 0 And 1 Are Not Probabilities - Less Wrong
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I think it would be interesting to develop probability theory with no boundaries, with no 0 and 1. It works fine to do it the way it's done now, and the alternative might turn up something interesting too.
You might want to check out Kosko's Fuzzy Thinking. I haven't gone any further into fuzzy logic, yet, but that sounds like something he discussed. Also, he claimed probability was a subset of fuzzy logic. I intend to follow that up, but there is only one of me, and I found out a long time ago that they can write it faster than I can read it.