As an aside...If there is a good resource on how to determine probabilities on your own that would also be a nice reference tool.

1. Consider the exact types of symmetries where different puzzle states count as the "same" case. For example, for last layer algs,

*usually* the reductions you care about are (what I call) pre-AUF and post-AUF (which are different things!). Depending on situation, you might also want to reduce by mirror symmetry and/or by inverting.

2. Count the number of cases without any symmetry reduction. (Usually this is just multiplying the number of possible corner orientations, possible corner permutations, etc. together. You might have to divide by 2 to account for corner permutation parity and edge permutation parity always being the same on a 3×3×3, but this doesn't apply to CxLL since you're completely ignoring edges.)

3. Classify the cases based on how symmetric they are. More symmetric cases are "less" likely

*after* reducing by the relevant symmetries, e.g. a case with 4 symmetries will be 1/4 the probability of a case with only 1 symmetry, for the reason that the less symmetric case can show up in more different ways (each of which have the same probability). (Note that the solved state is the most symmetric under the usual symmetries, which is also why skips are typically the rarest possible case (e.g. 1/72 chance of PLL skip compared to 1/18 for most other PLLs).)

And finally,

4. Think very hard about

*why* you want to calculate case probabilities. There almost always isn't a good reason to do this (beyond academic curiosity). It's meaningless to prioritise alg sets by case probability because (i) usually the people who think of doing this are trying to apply it to small alg sets like PLL or CMLL/COLL/CLL where prioritisation doesn't really matter and (ii) the vast majority of cases will have exactly the same probability (the highest possible: the one corresponding to trivial symmetry).

tl;dr 2/81 for every COLL case,

*except* skip (1/162), diag (1/162), H permuted (1/81) and H diag (1/81).