"tratar de + infinitive" = to try
"Quiero tratar de ser mejor." (I wanna try to be a better person.)
"probar a + infinitive" = to try, but implies a previous choice or decision
"No se si servirá de algo, pero voy a probar a ser mejor." (I don't know if it's worth but I will try to be a better person.)
Anyway both "tratar" and "probar" have other meanings:
"tratar" = to address, to treat...
"probar" = to taste, to check, to demostrate...