As far as I can tell from the current interface provided for setting up e-mail alerts for builds in visual studio team services, there is no way to set a condition on the status of the previous build.
I expect this is relevant to many development teams as teams will typically have a build server churning out builds frequently throughout the day and will want e-mail alerts of a failure. Following a failed build, it is useful to also have a success email for the next build. However, you don't want an e-mail for every successful build as you are only interested in this after a failure, the rest is just white noise.
So is there any way to create alerts conditional upon the previous build in visual studio team services, or more specifically to just get success e-mails after a failed build?
There isn't any way to do this with the alerts feature in VSTS for now. You can submit a feature request on VSTS User Voice.
And the alternative way to achieve this feature would be create an application/service to track the build event and send out email notification base on the build status you want via VSTS Rest API or TFS API.