I'm referring to this question: When do miners stop waiting for new transactions?
More specifically, this statement from the top answer:
"suppose you have a block header h1 on which you have already tried a billion nonce values, and a header h2 which has just been generated and on which no nonces have been tried yet. If you have the choice as to which one to hash next, which should you choose, for the greatest chance of finding a winning nonce? The answer is, it makes no difference - they both have exactly the same probability. So there is no harm in switching to h2"
I would have thought that the probability would be slightly higher for the first block (h1) as there are 1 billion nonces that you know do not succeed, i.e. fewer winning possibilities.
Complete newbie here and to the bitcoin world so apologies if I'm missing something obvious.