Fine. I was trying to answer your question "what do people mean when they say they're 33% sure that tomorrow it will rain". They mean that they find twice as plausible that it will not rain. It's just that you don't understand it as they do.

Anyway, I think you're getting the direction of the argument wrong. It's not that you have probabilities and force an interpretation of them as degrees of belief.

You start with real numbers representing degrees of belief (with an ordinal meaning only, a larger number means more plausible) and some "common sense" properties they should have to be "rational":

  - having identical information should result in the same degree of belief

  - the degree of belief in "not A" should be a function of the degree of belief in A

  - the degree of belief in "A and B" should be a function of the degree of belief in "A given B" and the degree of belief in B

The rules of probability _are_the_consequence_ (once the value of certainty is fixed to 1)

    p(A) + p(not A) = 1

    p(A and/or B) = p(A) + p(B) - p(A and B)

    p(A and B) = p(A|B)p(B) = p(A)p(B|A)

and the use of probabilities to represent degrees of belief is not something you come up with. It is derived from the assumptions above (which don't involve probability at all).