Someone already create
www.directory.iobut I think this site is only prank
Its good that guy who make this site didnt
implement address search option
So is it his website real or just fake?
Do we have to worry about is?
Its real, but you dont have to worry about it. They dont have a database with all keys (there is not enough storage space on the planet for that), they just generate them on the fly.
The chance is extremely low, you better worry how to keep your paper wallet safe & secure.
If you worry about it, split your bitcoin to multiple addresses or using multi-signature address
So if two people have the same private key, they have the same wallet??
No, wallet is the software that handles the private keys for you.