I like the way Rav Amiel sets up this question in his Midos l'Cheiker Halacha: The famous sugya of tukfo kohen (B"M 6) speaks about an animal counted for ma'aser beheima which then jumps back into the pen of uncounted animals. This ruins the entire rest of the count, because from that point onward every 10 animals counted might have in the mix the one animal which jumped back in.
Tosfos and other Rishonim ask why this should be -- why not say that the one animal already counted is bateil to the rest of the herd which still needs to be counted?
The Rishonim answer that this is a special din based on a gezeiras hakasuv of "asiri" - vaday v'lo safeik. The designation of the 10th animal as ma'aser must be done with certainty; since any 10 animals taken at random from the herd might contain the one animal that shouldn't be there, there is no longer any certainty to the count. This is one of the popular sources that indicate that rov does not resolve uncertainty / safeik -- it merely allows us (in usual circumstances) to act or draw conclusions despite the latent uncertainty which remains. IOW, in yeshiva jarogon, rov is just a hanhaga, but not a birur.
Now for the fun. The gemara (Kesubos 15) presents the din of kol kavu'a k'machtza al machtza using the following case: let's say you have nine frogs and one sheretz in a mix and you stick your hand in and grab one. Even though the odds are that you touched a frog, the Torah has a chiddush that where you jump into the ta'aroves mixture (as opposed to, for example, one of the creatures jumping out at you) we treat the safeik as a 50/50 chance. The special din of kol kavua essentially eliminates the din of rov and levels the playing field of probability.
Here's the catch: the laws of how to treat safeik tumah differ from other areas of halacha. So long as the safeik arises in a private domain, no matter how many sefeikos are involved, the halacha is that safeik tumah b'reshus hayachid is tamei. So why do we need this special din of kol kavua? Since rov does not eliminate doubt --the safeik still remains, just the odds are tilted to one side over the other -- every case of safeik tumah b'reshus hayachid should be de facto tamei even without the rule of kol kavua! The very case of the mixture of frogs with a sheretz which is the paradigm of kol kavua seems to be a case where the chiddush is unnecessary to arrive at the conclusion.
Rov, kol kavua, tukfo kohen -- it doesn't get better than this : ) I won't spoil it by posting an answer just yet.