I store almost all of my assets using MEW because I like its functionality, but I'm worried about the fact that someone can still pick up the private key to my wallet. One day I wanted to open my wallet and mis-typed all the characters from my private key, but in the end I was able to open another Ethereum wallet, which turned out to be empty. But nevertheless I was able to open another wallet with my private key where a few characters were changed. This alarmed me. After all, someone will be able to pick up, purely by chance, the private key to my wallet in the same way. I am concerned about this issue.

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 Such a probability is one in a million, I think that you will no longer succeed in such a trick if you try to repeat it thousands of times. Maybe it was just a wallet glitch that showed you zero balances for a non-existent wallet.