Statistics Question - I Think??

Ok. Here goes. I would like to get an answer about probabilities.  How
do those little percentage screens on the World Series of Poker work? 
You know what I am talking about, one player has two jacks and another
player has a pair of nines and a third player has suited jack, 10.  
Almost instantly, the screen says who has the greatest probability of
winning.  Please give me a good statistical answer on this one... Is
it conditional probabilities?

Sure it's a statistics question.

A computer employed by ESPN computes the chances of each person to win
the hand, based on the cards that have been revealed and the cards
that are still left in the deck.  TV viewers and the ESPN crew have
the advantage of seeing other players cards so the percentages are
truer.  The player have no way of knowing the other players cards so
they don't know the percentages until the cards are revealed.

There are many poker learning aids that will provide you with a basic
chart of percentages of various starting hands versus other hands.

I'm no statistician but I'm sure one of the researchers will provide
an example of how to compute a hand.

BTW, if you watch sometimes a skilled player will blurt out a
percentage that they have computed or memorized when they see the hand
they are playing against.

Hey thanks for the the behind the scenes look.  I tried to play online
once and lost all my -- fake money -- within 5 minutes.  Not as easy
as it looks.

Check out this cool odds calculator:

http://www.cardplayer.com/poker_odds/texas_holdem/index.php