This question is inspired after reading How are ethereum addresses generated?
This is the section of interest
There are three main steps to get from private -> address:
- Create a random private key (64 (hex) characters / 256 bits / 32 bytes)
- Derive the public key from this private key (128 (hex) characters / 512 bits / 64 bytes)
- Derive the address from this public key. (40 (hex) characters / 160 bits / 20 bytes)
From this simplified explanation, it seems that if you create a random private key that someone previously generated, you would be able to gain access to their account. This is clearly not the case since many accounts have been created and I have never heard of this happening. So, what exactly am I missing here?