OK, so basically ad-hoc/greedy. That can get you into, well, issues :-) There are methods where you first adjust away impossible statistics (if you have quals a,b, then P(a)P(b) >= P(a AND b), but if your estimates come from multiple places this might not hold[1] -- so you need to fudge one or more of those before proceeding), and then combine them optimally using Newton-Raphson. It's pretty neat. But it does require a matrix library and stuff :-)

[1] Similarly, you can sometimes guarantee stuff like P(a AND b) <= 1/n due to a unique multi-column index, which can also inform some of your sub-estimates.