Good afternoon! Such a question is interesting, and with what probability can you accidentally get a seed phrase that is associated with a real address with a balance in the bitcoin blockchain?
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The probability asked will I believe depend on the input entropy in the seed phrase for the key derivation function; on how many "real address with a balance in the bitcoin blockchain" have been generated with it (it's improbable to find others); and on how many attempts are made. All this is so bitcoin-specific that there was no choice beside migration from Crypto-SE, where the question and a first answer originated. – fgrieu Nov 27 '23 at 05:26
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Does https://bitcoin.stackexchange.com/q/8804/5406 answer your question? – Murch Nov 27 '23 at 18:07
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Seeds are usually on the order of 128 bits of entropy.
2^128 = 3.4028237e+38
That's 38 zeroes.
Furthermore, each attempt is somewhat costly because it uses a good derivation function. So you can't even try very many.
This is for entire wallet collisions. For addresses, Bitcoin uses a 160 bit hash which is an even harder ordeal.