AFAIK, there is not SET ANSWER for a block. You solve shares for the WHOLE NETWORK, and if you solve the block, it gets attributed to the pool. Blocks aren't given a block to play with and hash until a given share is right. I could be wrong, but I believe this is the proper explanation.
That's completely irrelevant, this is an analogy about chances, not about uniqueness. Chance is chance. The probability for me to draw a red ball out of an urn with 10 red balls and 990 white balls is exactly the same as the chance to draw a red ball out of an urn with 1 red ball and 99 white balls.
Additionally, what Wolf0 said is also true.