Hummm, the purpose of the rehashing is to get a target a hash that is equal or less to the real input hash so with that example aren't we going to get anything above the hash (if true )
That's not how hashing works. You might've misunderstood something there. For starters, there is something known as the Avalanche Effect in Cryptography, for which the slightest change in the input results in an entirely different hash. You can verify it by hashing 100001 and 100011, they are completely different hashes and the latter hash is actually smaller as compared to the former when converted to hex.
The probability of the hash meeting the target is equal with every single nonce in the range.