You never want to delete a program, always uninstall it. You will need to run the Adobe script cleaner, reboot and download CC.
Curt & Mylenium are correct, This is because you deleted the Ps app not uninstalled it. So when you try to download, it shows you that Ps CC is already installed.
Run the Cleaner tool to remove Ps CC :http://www.adobe.com/support/contact/cscleanertool.html . Restart your system and then try installing Ps again.
If it does not work please let me know, I would try to resolve it over a connect session.