des key collision?

I am a noob at des/3des.
I know that finding a des key for a random plaintext(hex):encrypted(hex) pair is 1/2^8 (64-56) chance, but is there any chance of having 2 keys in the same keyspace?
(like des(0x00, 0x88888888)=des(0x00,0x69696969)

Or is it certain that the key is unique?