Making a shared calendar 'Private' is easy!
FROM THE WEB APP
Step 1: Go to your Calendar > Calendar Sharing Icon
Step 2: Find your ICS link and Click "Show Details".
Step 3: Select "No, Only Show Events as 'Busy'...".
Step 4: Done.
FROM THE MOBILE APP
Step 1: Tap on Menu > Calendar > Calendar Sharing Icon
Step 2: Tap on the name of the user you want to edit.
Step 3: Disable the "Show Details" option.
Step 4: Save/Close.
