You can deploy your entire setup in Azure by creating VM's. You can create 3 VM's in Azure which are part of same vnet. Promote 2 VM's as domain controller. In this set up one VM will be primary DC.
Usually, active directory doesn't work in active and passive mode. When client want to reach any DC, there is a DC discovery that happens. Always the nearest DC will be contacted to handle the request.
As per your question if one AD goes offline, automatically 2nd VM will take over to handle the requests.
There is always a replication between domain controllers in an environment. Below is the article that talks about on how the replication works.
https://learn.microsoft.com/en-us/windows-server/identity/ad-ds/get-started/replication/active-directory-replication-concepts#BKMK_1
To know more about how DC discovery works you can refer below article,
https://social.technet.microsoft.com/wiki/contents/articles/24457.how-domain-controllers-are-located-in-windows.aspx
Let me know if you have any further questions.
Please "Accept the answer" if the information helped you. This will help us and others in the community as well.