Absolutely and definitely

I found these two adverbs are quite similar.
Example 1.
A: Do you think Maria will be here?
B: Definitely not. ----> Is it okay to say “Absolutely not”?

Example 2.
A: Do you let your kids travel alone at night?
B: Absolutely no! ----> Is it okay to say “Definitely not”?

Example 3.
This cake is absolutely delicious. —> Is it okay to use “definitely”?

Thank you!!!

Examples 1 and 2 both sound fine either way, but example 3 would sound weird if you said ‘definitely’.
Taking the literal definitions, ‘absolutely’ means something like ‘to the maximum possible extent’, whereas ‘definitely’ means something like you strongly agree with the claim and are disputing someone else’s (real or hypothetical’ claim to the contrary. For instance:

A: Fifty one is a prime number.
B: Fifty one is definitely not a prime number, it’s the product of three and seventeen.

I guess the cake one could go something like:

A: This cake is pretty tasty.
B: This cake is absolutely delicious (not just good, but extremely good).

Or (contrived example)…
A: This cake is not delicious
B: This cake is definitely delicious, you just can’t tell because you just got back from the dentist and the oral anaesthetic hasn’t worn off.