Though are you sure the files are not already MP3s and you haven't just got real player set to be the default player for MP3s which would mean windows shows them as being real player files.
I've used zamzar with no problem... if you are concerned, set up another Hotmail address for this process...
Incidently, if zamzar won't convert your RealPlayer file, find the track on youtube (with good sound quality) and paste the .url into the zamzar window rather than uploading a file from your PC. That'll work...