Why does Oedipus believe that Teiresias can provide him information on the death of Laius?

Before Teiresias appears in Thebes at Oedipus's request, Creon returns from the oracle of Delphi, to which Oedipus had sent him to find out why Thebes is suffering so much. The ancient Greeks believed that Apollo was the god of prophecy and that he was the original source of the responses the Delphic oracle would offer to those who came to her with questions. It is she who tells Creon that the reason for the suffering in Thebes is that the murderer of Laius, the former king, was never found and prosecuted. Oedipus, then, decides to launch a full investigation of the crime. However, he doesn't really know how to begin; luckily, the Chorus offers him a suggestion: "For the quest, 'twere well, methinks / That Phoebus, who proposed the riddle, himself / Should give the answer—who the murderer was."
In other words, they believe that, since Apollo (Phoebus) was responsible for the oracle's message, asking someone else with the gift of prophecy, who would also be favored by Apollo, might be a good start. The chorus says, "if any man sees eye to eye / With our lord Phoebus, 'tis our prophet, lord / Teiresias." Therefore, Oedipus doesn't call Teiresias just because he is a prophet, but also because his ability to see the future and interpret omens would have come from Apollo, the same god who compelled the oracle to tell Creon what to do. If any god can help them, it is Apollo, and since Teiresias is Apollo's mouthpiece, so to speak, Oedipus calls for him.

The play Oedipus Rex was written by the Greek playwright Sophocles, who appears, from the limited available biographical evidence, to have been a conventionally pious man of his period. Both Sophocles and his audience would have believed in divination, the possibility of certain expert seers or oracles knowing the will of the gods and being able to interpret various signs to learn of things normally outside human knowledge.
Teiresias is a seer, dedicated to the service of Apollo, the god of prophecy. The gods have granted him the gift of prophecy, including a limited ability to see both past and future. Thus Oedipus asks him about the death of Laius because of his skill at prophecy. As Tiresias does, in fact, correctly identify the murderer, Oedipus was correct in asking him but misguided in not immediately believing his answer. In all of the plays in which he appears, Tiresias' answers to questions are always correct, although sometimes difficult to interpret at first.