Very slow answer here, but you can always make your calendar private, which will prevent anyone from searching for and seeing your events.
You can also make your calendar public, but default to only show
When you select Make this calendar public, all of your events will
appear in the public search results of Google Calendar and Google.
Additionally, others will be able to view the calendar and its public
events with your Calendar Address, or by adding the calendar to their
Making your calendar public and selecting See only free/busy (hide
details) means that your calendar information will not appear in the
search results of any Google Calendar or Google search. Additionally,
only your free/busy information will be visible to those who access
your calendar at its address, or by adding it to their 'Calendars'
To keep your calendar private and only shared with the people you
designate, be sure the 'Make this calendar public' option is not
selected. For information on sharing your calendar with specific
people, please visit this page.