The Lost Prince

One baby is a prince: One high ranked official has exchanged him with an animal when he was born. So when the emperor saw the animal, he thought that the queen has given birth to an animal, he chased her away. As for the baby, he got rescued by one of the servants but was abandoned in the street.
One baby is the son of a prostitute: She fell in love with a man and gave birth to this baby. But her lover abandoned her, so when she saw the prince in the street, she put her baby beside the prince and went to commit suicide.
One baby comes from a poor family: The family couldn't raise him, so sold him to another family. Actually, the wife of the high ranked official feigned a pregnancy, because she was afraid her husband would marry another woman. So she bought a baby and did as if she was pregnant. But when the maid passed by and saw the two other babies, she exchanged one of them.
The three babies are boys and are born on the same day. One becomes the son of a high rank official, the other two were raised by a tricky man. Which one is the prince?