Malcolm was born and raised to be the Emperor -
Or at least, he was supposed to be. He was so sure that he would be the successor to the throne, especially considering that he was the first-born son and that he had trained at a very young age to be the next ruler. There was not any strong competition around, either.
Caspian is not suited for the role.
Not only is he not as active as him when it comes to fulfilling the qualifications needed to be seen as the empire's Crown Prince, but he himself does not show any interest in that path. That's why he's more than willing to support him in his endeavors in the research institution. He's not a threat at all.
Then, there was Eric - the prince who was born blind.