How does a paper wallet actually work?

I have just created my first paper wallet for Monero, using the direct zipfile link:

I did it all offline. It was an interesting process to go through. How does the offline wallet creator, since it is not networked when the wallet is created, ensure that two people in the world don't create the same wallet address by accident?

(Note: the url redirects to another url, namely: Not sure if that is supposed to happen.)

submitted by /u/theprivacydad
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