What is the relationship between a Bitcoin Private Key / Public Key / Address?
Using Elliptical Curve Digital Signature Algorithm (ECDSA), the private key is used to generate the public key, a secure hash function is then applied to the public key and a checksum appended to produce a Base58 formatted bitcoin address.
A private key collision is theoretically possible, but practically impossible due to the sheer number of them available on the network (quadrillions+).