I assumed that someone generated it, ended up with a private key and then declared it destroyed.

You start by

**generating** the private key.

Then you

**calculate** the public bitcoin address from that private key.

The results of that calculation are completely unpredictable, so for any given private key the resulting address will be one of 2

^{160} possible bitcoin addresses, and which address it will be is completely unknown until you calculate it.

So, if you start by wanting a specific address, all you can do is keep trying different private keys and see if the resulting bitcoin addresses match the address that you want. Since each private key has a 1 in 2

^{160} chance of being the address that you want, you have a 0.0000000000000000000000000000000000000000000000684% chance of finding the private key for that specific address each time you try.

You have a better chance of winning a major national lottery (such as the PowerBall in the U.S.) multiple times

**in a row** than you do of starting with a specific desired bitcoin address and stumbling on the correct private key in your lifetime.