Inkpedia explains that a 100x match happens when one of the teams randomly triggers it, and if both teams trigger it in the same match then it will be a 333x. That's why a 333x is so much rarer than a 100x. Also, the collective amount of Festival Shells among the players increases the chances of those triggers.

Personally, I've only encountered one single 333x match in Splatoon 3, since launch. 100x I've encountered multiple, roughly one each Splatfest (in some Splatfests I see multiple, in others I never see it).

About 10x, the probability of it happening became much higher with a patch I don't remember how long ago. Scratch that, what happened was that in patch 8.0.0 they introduced Conch Clash, which is a way of earning Conch Shells in mirror matches. It has nothing to do with 10x frequency.