If I use the TestNg priority option, what would be the order of execution for tests?

Here you have to consider 2 points : If you are not using any TestNG priority in your test method then TestNG assign by default priority=0 to the Test Method If there is same priority assign to test methods then execution order will be alphabetically. So in your case it is adding priority=0 internally to your ztestNP() methods

@Test(priority=0)
public void ztestNP() {
    System.out.println("Test NoPriority- Revision");
}
So your output what you are getting is correct.
Now if you want to test execution order of same priority methods(will execute in alphabetical order)
e.g.
@Test(priority = 1)
public void btest1() {
    System.out.println("Test Priority One- Revision");
}
@Test(priority = 1)
public void atest2() {
    System.out.println("Test Priority Zero - Revision");
}
@Test(priority = 0)
public void ztestNP() {
    System.out.println("Test NoPriority- Revision");
}

Then output will be :

Test NoPriority- Revision

Test Priority Zero - Revision

Test Priority One- Revision