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What's the chance that some person will ever solve the same 7x7x7 scramble as another person? (apart from scrambles that are posted to solve, or at competitions of course)

I think it never happens, and that every scramble is unique.
There are way too many combinations for that to happen.

@5BLD: Well, what I meant is how likely it would be for two people to have the same scramble.

There are more different 7x7 scrambles than there are atoms in the universe.
Everytime you scramble a 7x7, be proud . Only you have ever scrambled it into that position(Unless you are really,really,really,really,really unlucky)

Tao, if that big number is the number of possible permutations, then the probability of doing the same solve (I'd guess) is just one in that number.... since the first person has nothing special about their scramble there is no probability associated with it (other than 1), so the second person has a 1 in xxxxxxxx chance of having the same one.

Tao, if that big number is the number of possible permutations, then the probability of doing the same solve (I'd guess) is just one in that number.... since the first person has nothing special about their scramble there is no probability associated with it (other than 1), so the second person has a 1 in xxxxxxxx chance of having the same one.

Solve?
There is an infinite number of ways to solve a given scramble, if you think of it mathematically. However, if we factored in the maximum number of turns that are likely, etc. You could work it out.
Yes, I'm too lazy to do the maths.

Assuming no one has ever done the same scramble before, it's

(the number of scrambles anyone has ever gotten on the 7x7)
------------------------------------------------------------
1.95*10^160

or

(the number of scrambles anyone has ever gotten on the 7x7)
------------------------------------------------------------
19,500,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,00,000,000,000,000,000

Edit:
My guess is that anyone who has done a 7x7 solve combined have probably done a total of around 50,000 to 100,000 solves/scrambles. So the answer to your question could be about :

Assuming no one has ever done the same scramble before, it's

(the number of scrambles anyone has ever gotten on the 7x7)
------------------------------------------------------------
1.95*10^160

or

(the number of scrambles anyone has ever gotten on the 7x7)
------------------------------------------------------------
19,500,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,00,000,000,000,000,000

Edit:
My guess is that anyone who has done a 7x7 solve combined have probably done a total of around 50,000 to 100,000 solves/scrambles. So the answer to your question could be about :

What's the chance that some person will ever solve the same 7x7x7 scramble as another person? (apart from scrambles that are posted to solve, or at competitions of course)

I think it never happens, and that every scramble is unique.
There are way too many combinations for that to happen.

@5BLD: Well, what I meant is how likely it would be for two people to have the same scramble.