Another way to ask this question is, what are the odds of any two people having the exact same private key at any time?

The explanation for this question is pretty interesting, but to make  long story short, you have a better chance of winning the lotto 9 times in a row.

Bitcoin private keys uses SHA-256, which is the number 2 to the 256 power. Which is an unfathomably large number.
If you counted all the grains of sand on planet earth and all the drops of water in the ocean, you would not even come close to that number!


More detailed explanation:

https://www.youtube.com/watch?v=2eZ5DP2P5As