You have two options.
One is to use javascript but that is messy and problematic.
Best to post to PriorityManager.php
then that looks at the priority and includes the appropriate file. The variables etc will be visible to the included file
so
in the html
<select name="priority">
<option value="One">Priority One
<option value="Two">Priority Two
<option value="Three">Priority Three
</select>
and in your php script
include("Priority" . $priority . ".php");