Mining difficulty and such

so.. I've tried to find a clear answer but I could not, or maybe I was to stupid to understand it ;)

form what I gather no matter the rig, for each and every one of the hashesh produced the chance of that beeing the winning one is the same - correct?

and if so, how come best share reported by cg miner grows in time every time from 1 or 2 and not starts once in a while with 4k

and if not.. well I'm lost..