I would think about tailoring your application to suit the university. Look at the faculty at various universities and see what probability theorists they have there, and start thinking about where you could see yourself working. Of course, this is extremely difficult to determine so early on in your academic life, but it's a good way to separate yourself from the pack, especially for Top 20 universities. They are essentially wanting to hire you as a researcher, so you want to show them that you want to contribute in a useful way.