"X combinations of being dealt...XX"

Hey everyone... quick question... often when I'm putting opponents on a hand and trying to calculate the number of hands I beat versus the number of hands that I beat, I often find myself tripping over the numbers...

For example I hold KK and I put the opponent on another High pocket pair... well there are 6 ways of being dealt AA and there are 6 ways of being dealt KK (of which my hand prevents 3 of them) and 6 ways of being dealt QQ, JJ, 10-10

So...

Part 1) I am ahead of 18 possibilities, tied with 3 possibilities and behind 3 possibilities.

Part 2 (Where I fall down) Of the hands that I am ahead, there are 6 possible cards that can come to beat me (a card to make trips) ... so that is 6:48 or I'm an 8-1 favorite?

Of the hands I am behind, there are two cards that can rescue me (another K) so that is 2:24 or I am a 21-1 underdog?

Part 3... When I am ahead, I will win, 78.5% of the time. When I am behind, I will win 5% of the time... so I have a 83.5% chance of winning?

Is that correct? Am I doing this right? If so, is there a way I can get there quicker? Some system that I can program into my brain? Or am I only going to get better at it by sitting down with a pencil and paper and running through scenarios?

This is a simple scenario, I can't imagine calculating flushes, straights, or other scenarios beyond pairs when I am sitting at the table...

I've searched for other posts, but apparently my search terms aren't hitting the mark.
Any help is appreciated!

Thanks!