Our calendar architecture makes this pretty simple.
Our calendar architecture gives account administrators the ability to control the access (visibility) and read/write permissions for each calendar. If you don't want a particular user to view content on a particular calendar, then don't give him or her a role on that calendar. For more information on calendar access and user roles, give this deep-dive article a read.
You can also select the Hide From Shared Calendar option in the Content Item Slide-In, while you are adding your content item (reference photo below) or within the Sandbox > Details section. Selecting this option hides the content item from anyone who is not the owner or assigned to the content item.