I don't know how to do the calculations, but I made a computer simulation. You're dealt Ad 7d and you look at a flop. The results are based on the ranking of your final hand (hole + flop) and also the state of the flop (so you know if "One Pair" means the board paired OR if you hit your card.)
My PC's RNG probably isn't that good, so these results aren't perfect... but they should be a reasonable ballpark.
<font class="small">Code:</font><hr /><pre>
200000 Trials
--------------
52.514% High Card
27.296% One Pair
13.472% One Pair (Pair on board)
2.103% Two Pair (Pair on board)
2.054% Two Pair
1.409% Three-of-a-Kind (Pair on board)
0.804% Flush
0.233% Three-of-a-Kind (Trips on board)
0.105% Full House (Pair on board)
0.011% Four-of-a-Kind (Trips on board)
</pre><hr />