If you generate a random private key in the range 1 - 2^256 the odds that you will get a value that is not in the valid range 0x1 - 0x0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364140 is 1 in 267776665566007192515705986938822075896 ... nearly impossible