LAST EDITED ON 10-29-11 AT 05:50 PM (EST)Ummmm, no.
You're viewing each rock as distinct. But 7 of the 8 rocks are the same, therefore the order of those doesn't matter.
Here's another way of putting it. If each person has a 1 in 5040 chance, then they total an 8 in 5040 (i.e. 1 in 630) chance of any one person getting a purple rock, which isn't correct, because there's a 1 in 1 chance of 1 person getting the rock. (Someone HAS to get the rock).
Or, to put it another way, there are only 8 possible combinations (you're thinking permutations, but they're combinations because the order of the non-purples doesn't matter) of outcomes:
Pxxxxxxx
xPxxxxxx
xxPxxxxx
xxxPxxxx
xxxxPxxx
xxxxxPxx
xxxxxxPx
xxxxxxxP
The probability, as you say, changes as each person draws, but not in the manner that you calculate--it gets more likely, not less, that you get a purple rock. But this is irrelevant, because they don't reveal until everyone has drawn, so everyone has the same probability of drawing a purple rock from the start.
Don't play Russian roulette with only 1 bullet in an eight-chamber revolver. You have a 1 in 8 chance of shooting yourself, not a 1 in 5040.