With this Swantide Workflow, you can set when a Case Owner should get an Email Notification based on the Case's Priority.

In this example, I will be enabling this Workflow to email the Case Owner whenever a Case Priority is set to "High" as my variable input.
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When I submit this Workflow to my Salesforce environment, every time a Case is created or updated and the Priority is set to "High" then an Email Notification will go to the Case Owner.

When this is done, the Email Notification will look as such:
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Simultaneously, the same thing will happen if a Case is Updated to being a High Priority Case.