Final answer:
Oedipus believes that the testimony of the shepherd, who was with King Laius when he was killed, might prove him innocent by confirming that Laius was killed by bandits and not by Oedipus himself.
Step-by-step explanation:
According to Oedipus, the one fact that might still prove him innocent is the exact circumstances of King Laius's death. Oedipus clings to the hope that the shepherd, the sole survivor from Laius's entourage, will confirm that Laius was killed by bandits at the crossroads, which would mean Oedipus was not the killer.
When the messenger from Corinth arrives with news of the death of the king there, Oedipus finds temporary relief, believing part of the prophecy to be untrue.
However, the shepherd who saved Oedipus as a baby is the same that witnessed Laius's death, ultimately bringing the truth to light - the truth that Oedipus had indeed fulfilled the prophecy by killing his father and marrying his mother.