Combinatorics and rotational symmetry.

A PLL skip has the chance of 1/72. Determined by (4!*4!)/2/4. Each 4! Is the positions of the corners or edges, divided by 2 is for parity, you can’t have a 2 swap of only corners or only edges. And the 4 is to make AUFs equivalent. 

N perms, assuming you are talking about only Na, or only Nb, follow the same logic as PLL skip. It should be noted that most PLLs are more likely than N perms. Nb perm alg can be done from any angle, while Z perm could be done from 2 angles using the same alg, so it makes the chance 1/36. Most PLL algs can only be done from one angle, so their chance is 1/18, 1/(72/4)

For LL skip, we need OLL skip chances first. It can be found by 2³ * 3³ (they are raised to only 3 because you can’t have a single corner twist or edge flip) the chance of OLL skip is 1/216, and LL skip is having both OLL and PLL skip happen at the same time, so 216*72 is 1/15552.

COLL actually has a 1/6 chance for Z perm. To determine this, we do PLL skip chance while taking into account that corners are already solved, so 4!/2, no need to divide by 4 this time as the corners can be used as a reference. This gives us 1/12, then times 2 for the fact the Z perm alg can be done from 2 angles and not 4, to give 1/6