How do professors usually discover "new" research interests?
Here are a couple ways that have resulted in new research directions for me:


Reading a paper/book. Reading a paper/book can inspire new ideas. You may find that a paper is missing something, or you think of a way of doing it better, or perhaps you can combine the ideas in the paper with something you already know.
Obtaining funding. Often funding is obtained in groups, generally to inspire collaboration and cross-fertilization of ideas. As a result, one is forced to venture into new territory.
Talking to a colleague (generally from other institute). Simply chatting with someone at a conference or when visiting another institute can inspire new research directions. They may have a problem; you may have the tools to solve it.
Changing job. This brings you in contact with new people who have new problems. Collaborations my result from conversations in the coffee room, or by going to research discussions within the new department.
Following up on something a student has done. You may set a masters student, for example, to look at something you find interesting, but have not yet had time to explore in depth. The student may come up with something useful, but then leaves.