The set of possible solutions 2^256 and globally in the time period of a block being solved a negligible percentage have been completed.  However there is no 1:1 mapping between inputs and hashes in a hashing function.  An infinite number of inputs can produce the same hash. 

Routinely within one block "window" the two elements of the blockheader that are changed are the timestamp, the merkleroot hash, and the nonce.  That provides 2^320 potential solutions.   Any potential progress is so negligible that for all practical purposes it can be considered zero and thus each attempt is independent. 

https://en.bitcoin.it/wiki/Block_hashing_algorithm

Each hash has a 1 in (difficulty)*(2^32) chance of solving a block.   At current difficulty that means each hash has an independent chance of 1 in  52,198,505,828,311,400 chance of winning the block jackpot.   Each hash/ticket is checked and discarded. If it doesn't solve the block much like a losing lottery ticket there is no progress (in any usable sense).  You are just as far from wining the jackpot on the next ticket.