(Sorry for my bad english I hope I can help you.. )
--> Close Steam. Now go into your Steam folder and delete the "ClientRegistry.Blob" file. Now open Steam. It will update.
Now when you are Online in Steam, open Modern Warfare 3. Then it will work :P
[Short Statement:] Close Steam, Delete the ClientRegistry.blob file, open Steam & it will work.
Okay.. Sorry for my bad english²