When the second bot realizes it knows the private key it has to create and broadcast a transaction with a slightly higher fee than the first not. When the first bot sees this transaction it creates a new transaction with a higher fee. And so on and so forth until the transaction is all fees.

The reason it has to do with brain wallets is because people are using insecure methods to generate a private key like taking a common phrase and hashing it with sha256 and using that as a private key.(this is what brain wallets are. https://en.bitcoin.it/wiki/Brainwallet#Obsolete_Brainwallet_Style). And these bots keep databases of billions of addresses generated this way and as soon as money is sent to one of them the race is on as to who can spend it first.