Mac App Store shows an update available for an app I didn't install Like this the picture below.

For the record, I did install some cracked apps which isn't available for demo from MAS to try them out. Could this be problem?

I'm on Mountain Lion, latest update. But I have experienced this problem on Lion as well.
According to http://hints.macworld.com/article.php?story=20120727110524438, you would want to check the /private/var/db/receipts/ folder for any files related to the app.

If the piracy messed with receipts, you may need exceptional records to clean up another app's receipt so this confusion might still be a result of your abuse of the normal app purchasing process.