Commenters minunderstand your problem and your argument for its solution. I take your problem to be "What could the probability of a mathematical proposition be besides its comparative likelihood of proof or disproof?
Perhaps the answer is that there are reasons besides proof to believe even a mathematical proposition. Empirical reasons, that is.
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Would someone be so kind as to direct me to a forum for epistemic rationalists?
[Who wants to talk to folks about important matters when they declare their willingness to deceive even themselves if it gets them what they want?]