Cmd.exe does not expect everything after /C or /K to be one quoted string.
Code:
C:\WINDOWS\system32\cmd.exe /K C:\BIN\ffprobe.exe -i D:\AVS\AVI\TEST.VOB 2> file.txt
should work as well, and also
Code:
C:\WINDOWS\system32\cmd.exe /K C:\BIN\ffprobe.exe -i "D:\AVS\AVI path with spaces\TEST.VOB" 2> "D:\Output path with spaces\file name with spaces.txt"