It is believed that the recently introduced feature has taken inspiration from Vivaldi Browser, which works on the DuckDuckDGo browser in its private mode.  To use the newly added functionality, you need to enable it by making certain changes to “about: config” bar. By default it is disabled and you will have to manually activate it. Follow the below steps to enable the Firefox Nightly mode on your system.

Download the latest version of Mozilla Firefox Nightly.

Open it and type “about:config” in the URL bar.Paste the below mentioned commands in the search box and set their values to true.browser.search.separatePrivateDefault.enabled browser.search.separatePrivateDefault.ui.enabledNow click on the “Options” button followed by the “Search” button and finally click on “ Default Search Engine.” A drop-down list of available options will appear on your screen. Choose the default search engine you wish to use for private browsing. 

So, this is it for now. Currently, this functionality is available only in the testing mode.  However, seeing the response towards this new Firefox Nightly feature, experts are anticipating that there are high chances that it will come as a default feature shortly unless any major complication pops up.