I may not know much about Bitcoin but I know a lot about computers. There is no way multiple instances of the same hash algorithm running on independent computers can avoid executing the same code on the same values. It's extremely redundant.
Once again making false statements as fact. Why not say "I believe it is redundant" or "I can't see a scenario where miners unknown to each other don't duplicate work accidentally?". You state you don't know much about Bitcoin but you feel confident about making absolute statements of fact about something you don't know much about?
The different computers (1, 2, a trillion it doesn't matter) use different inputs and thus (barring some isolated implementation errors) never attempt work which has already been attempted. Miners aren't hashing some random value, they are hashing the blockheader and Satoshi designed it so there would be no duplication of work.
https://en.bitcoin.it/wiki/Block_hashing_algorithmEven if everything else is the same in a block, the coinbase tx for each miner will be unique and thus the hash for that tx will be unique and thus the merkle tree will be unique and thus the merkle root hash will be unique and thus the blockheader will be unique.