Let's say the nonce is from 0~100, and each node has to find one nonce to satisfy the requirement. The attacker has to start at 0, maybe it's just the one he needs, maybe not. The probability is 1%. While for the public network, they may start at 50(cause they try the nonce all along), and the probability is 2% now. It seems clearly that they have different base point.
That's not how mining works.
Each miner is working on a different nonce, because each miner is working on a different block.
There is no guarantee that any of the nonce values will work. The miner that is "at 50" could continue all the way to 100 and still not find a working nonce. The miner that is starting at 0 may find their nonce before they get to 100.
Prior to calculating the hash, each hash has the same chance of success. It doesn't matter it this is the 1,000,000,000,000,000th hash that you've computed or the first hash that you've computed. The chances that the hash will be successful are the same.