You can refer to this guide for a general set of guidelines to address this issue. Some of the solutions depend on how Algolia responds to the no results behavior -- see this section.
In terms of how your UI handles an empty hits response however, this must be configured on your front end.
If you are using InstantSearch or another one of Algolia's front end libraries, you can use this guide to edit this (change the library to reference using the right hand drop down)