Ethically, should you report cheating that you learned of indirectly? Six classmates and myself have been in the same program for the past 2 years and one of them just informed me of another classmate that sits beside him of cheating on exams, so I informed the professor, and now that person may be kicked out of the program. 

Did I do right?

Why did that classmate inform me of the other persons cheating? I felt an ethical obligation, because of the program we are all in too disclose this information to the professor and did not want the burden of knowing on me.
For many types of moral situations, university rules actually require that you inform a superior as soon as you find out yourself, or you are also in violation.  It may be that the classmate who informed you didn't have the civic courage to report it but knew that you did.  It is precisely to break cycles of no one saying anything that the rules are set up in the way I just described.  

Or of course it may be that they were lying.  As long as you passed the full information to the professor about how you knew what you knew as well as what you believed you knew, it is now the professor's responsibility and not yours.  If there's anything you haven't already told the professor, I'd suggest contacting them again.