I know you love math, so math time!

There are four arrangements of 3 sexes, either MMM, MMF, MFF, FFF, since order among them doesn't matter. However, they don't have the same chance of occurrence. MMM and FFF have a 1/8 chance, while MMF and MFF have a 3/8 chance each.

So if you had MMM cats, the chance of also having MMM SOs would be 1/8.
If you had FFF cats, it would be the same 1/8.
For MMF, the chance would be 3/8 of an overlap.
For MFF, again 3/8.

So it can be said there is a 1/4 * 1/8 +6/8 * 3/8 chance of an overlap, which is 31.25% chance of overlap!

Another way to look at it, is that there are 8 arrangements of 3 sexes:
MMM
MMF
MFM
MFF
FMM
FMF
FFM
FFF
For each of those, there are 8 other arrangement of sexes on the other set, so a total of 64 combinations.
The MMM and FFF overlap with only 1 set from the other side.
The other combinations all have 3 matches.
So 2 matches, plus 3*6 = 20 mathches out of 64, 20/64=0.3125, or 31.25% chance.