The only people who can view a conversation are the people listed at the top of the conversation. To verify the people, click on the conversation title to pull up the conversation details popup. Click on the link next to the People header and you will see everyone who can view and participate in the conversation.
Note: If you see “Everyone” listed then any new team members added to the space would then be able to view the entire conversation, even comments that were added before that person was part of the team. This is a handy catch-up feature to allow new members to have a full picture of the space.
Note: Similarly, if someone is added to the People in the conversation, they will be able to see the whole conversation thread including comments that were made before that person was added to the conversation. This is a great feature for helping the new member catch up on the whole discussion.