R. Ba citing Rav Chisda: There are three people who are believed to testify immediately after they witnessed, a midwife, a caravan and a woman who can purify her friends...

A midwife - she is believed as long as the woman is still sitting on the birthing stool, as the pasuk states (Bereishis 38:28), "and the midwife took [a scarlet thread] and tied etc.'' (thereby declaring which of the twins was the firstborn).

A caravan - like R. Simon, the brother of Yehudah bar Zavdi said in the name of Rav - A child, as long as he is abandoned in the market, his father or mother can testify about his identity. Once he has been taken in from the market, we require two witnesses, and his father and mother act as two witnesses.

A woman who can purify her friends - like the Mishnah (in Maseches Nidah) - If three women were sleeping in one bed and blood was found underneath one of them, they are all tameh. If one checked herself and found herself to be tameh, she is tameh and the others are tahor.

R. Ba: As long as she checked herself within a day of the blood being found.