Severus Snape was not a foolish man so after hearing Dumbledore's story of how Alan Daniel Potter was the boy-who-lived he knew he would have a slytherin Potter.

James and Lily after hearing Albus say Alan defeated Voldemort forgot about Harry.

Harry was the real boy-who-lived he was certain of it, he was also sure that after the neglect and pain he would probably suffer he would be the wizarding world's strongest dark lord.

Severus had no idea how right he was but after all he was a slytherin, he would help Harry, who he knew would some day rule the wizarding world.