The probability of being dealt 3 kings on hand 1 then 3 aces on hand 2 is about 1 in 30.5 million.

The probability of being dealt:

KKK then KKK or
KKK then AAA or
AAA then KKK or
AAA then AAA

is about 1 in 150,000.

Add queens into your list of top rolled up hands and the probability of any combination is about 1 in 10,000.

Calculating the odds of not improving takes a little more work.

(Ignoring the flushes/straights there is a 60% chance you will not make quads or a full house once dealt a rolled up hand)

The odds of not improving and holding up further depends variables you haven't listed.