If you have Final Cut Pro, then you should have Compressor as well. I don't know for sure if Compressor will convert asf files but it's easy to find out. Import the file into Compressor, and drag one of the preset formats into the batch window, then choose a destination. If it's a large file, you can mark in and out points in the preview area on the right side of the interface to transcode just a short portion of the file. You can export it to any of the formats in Compressor, including H.264, mp4, dv, and others. If you're able to view your test video as an mp4, just remove the in and out points and export the entire file. If not, you may need some other kind of converter, which maybe someone else can suggest.