Why do the Dementors care about Sirius escaping?

Sirius is only one of many prisoners in Azkaban, and is likely one of the more lost (or at least the Dementors perceive him as more lost because his emotions seem inhuman) so why is it such a big deal to them if he escaped? First off, I totally understand that they would be eager to go out and search for him, because it gives them access to hundreds of fresh people to feed off of, but that’s not really what I’m talking about. I recall the Dementors being described as furious and determined to recapture Sirius, but why? Can Dementors even feel emotions like rage or determination? Do they even care about their positions as prison guards?

The soviets even influenced the Harry Potter Series

I'm autistic and my special interest is the Harry Potter books, these are all the ones I have so far

Favorite character?

Going through the books for the first time, 5 down 2 to go.

Don't break rules

Discover this masterpiece tonight

Could Dumbeldore have just cut his hand off?

Would this have stopped the curse? If not, why?

Waiting for the Knight Bus

Challenge 3: Make me have even a shred of respect for the Malfoys.

The Dursleys and Umbridge were fun. Lets see what else you Potterheads can come up with!

Just a little drawing of how I imagined Tonks to look like