Creating new bitcoin addresses (and private keys) can be done completely offline which means I can, by accident, choose a public address which was already created by someone else in the past, right? I know the possibility of choosing the same address is almost 1/∞ but, even in the Powerball there is sometimes a winner.
If not, one of these explanations must be true:
I cannot choose already existing public address because the generator won't let me do this.
I will create the public address as well as the private key but, when someone sends bitcoins to that address, only the first wallet which was created by someone else in the past will receive the money. And my wallet will not be even seen by the network.
Or?
I couldn't find the answer for this problem hence I am asking.