Help with methodology needed please.

I was playing hold'em very recently - I flopped a FH, and at the end of the contest the other playing contesting turned over their cards and they had exactly the same hole cards (AKo). I wondered what the odds of this occuring are - two people flopping a FH with identical cards. I've seen from my boys book of knowledge that the prob of hitting a FH on the flop from two odd cards is 0.092% or 1/1,086.95. I need some help in calculating the odds of two players being dealt identical hands (ignoring the issue of suits).

In-play, and in general, I tend to use a "fuzzy" basis for calculating odds, ie for calculating the odds of a heart hitting the turn or the river with two in hand and two on the board being 9 (13 less the 4 in hand/seen) over 47 (number of unseen cards) multiplied by two (number of opportunities to show) over one - 9/47 x 2/1 = 18/47 or ~1.5-1. In this case I'd like the methodology for spot on.

I can calculate the prob of one of the other five players at the table being dealt one of the three remaining cards of the type dealt to me, but am unsure as to how to calculate the coincidence of that same player being dealt one of the three remaining cards that match my second. I can work out the prob of any player receiving the same as my second, but as their are five players should I be multiplying this by 1/5 as there is a 20% chance of the player who receives this card being the same player who received the identical first card.

It's a very long time since I dug into the maths to this degree.

Thanks in advance.

G.