Getting AA 3 times in a row is 1/221^3=1/10,793,861
Same 2 guys getting AA in same hand twice in a row depends on the question you're asking. If it has to be 2 specified players before any cards are dealt, it's (4/53*3/52*2/50*1/49)^2=1/270,725^2=1/73,292,025,625.
If it could be any 2 guys getting the first AA,AA, then it would depend on the number of players at the table. For a 9 handed game, the 1st AA,AA would be 1/270,725*36 (the number of different 2 player combinations you can make from a 9 handed game)=~1/7,520. Once 2 guys had gotten the first AA,AA, the next AA,AA would be 1/270,725. So, the combined probability would be ~1/7,520*1/270,725=~2,035,852,000.
As far as the spice girls part, I'd say the probability is none and less than none.