What immediately comes to mind off the top of my head would be if the other hands were AA, AA, and KK. You're drawing pretty slim in that instance, and if those were in fact the three hands you were up against then that's one heck of a story to tell... seeing 4 hands at the same time KK or better.
You'd definitely have more than 0.01% equity in that situation, but as far as winning the pot outright yeah that's probably going to happen around 0.01% of the time give or take (can't stove anything atm). I can take a couple of minutes to work out the exact probability since it would be relatively straightforward to do (only a straight flush to the K will win you the pot), but anyone could just stove it and get the precise figures that way so there's no real point.
If the hands were AA, KK, and QQ, and the aces and queens both happened to match your kings in suit, then you can never win that pot at all. Your overall equity would still be greater than 0.01% thanks to splits but it would be lower than in the AA AA KK scenario above.
As an aside, having literally 0% equity in a pre flop confrontation and no hope of even a split is very difficult to do. You need a minimum of 6 callers, and even then, coming up with the correct 7 hands to make this work is not a simple task. Heh.