Example 1
Brian is definitely going to see the new Marvel movie the day it comes out. He's the biggest Iron Man fan I know.
We've always been partial to The Hulk, but that's just us. In this heroic example, definitely indicates that there's no doubt that Brian will be in line at the multiplex on opening day.
Example 2
Mrs. Glue could tell by his answers on the To Kill a Mockingbird exam that Lionel definitely didn't read the book.
Lionel's missing out: To Kill a Mockingbird is a classic. Here, definitely is the correct word because it means the same as clearly.
Example 3
The protestors defiantly sat in the cafeteria for the entire school day. They'll do it again tomorrow, and every day after, until the lunch ladies put dinosaur chicken nuggets back on the menu.
We can think of no nobler cause for exercising one's rights than dinosaur chicken nuggets. In this patriotic sentence, defiantly is the right word because the students are boldly challenging authority with their sit-in.