Interval/affine arithmetic are alternatives which do not make use of probabilities for this these kinds of calculations.

https://en.wikipedia.org/wiki/Interval_arithmetic

I think arbitrary distribution choice is dangerous. You're bound to end up using lots of quantities that are integers, or positive only (for example). "Confidence" will be very difficult to interpret.

Does it support constraints on solutions? E.g. A = 3~10, B = 4 - A, B > 0