Based on my rudimentary understanding of Bitcoins and altcoins, network difficulty is adjusted by asking the network to target a hash smaller than a specific number, which translates to calculating nonce for a hash with a certain number of zeros prefixed to it.
Since hash values are supposed to be uniformly distributed, I don't understand why targeting a hash value with a specific number of zeroes is any more easy/difficult than targeting any other hash (not the hash value of the content without nonce obviously). I think targeting any of the possible hash values, except what the content already hashes to, should be equally difficult. Why is that not the case?
It's very likely that my understanding of Bitcoin network difficulty itself is wrong, in which case, could you please explain that to me?