Space available deadlines: How do they actually work?

Basically, I missed the application deadline at my top-choice program ( at UC Davis for reference) by 20 hours which puts me in the space available consideration pool. I am wondering what implications this has on my chances of admission. I understand the general process, that the on-time application pool is considered first, and the space available is considered only if there are still extra spots. What I am unsure about if it is extremely rare that there are any spots remaining or if it is standard when they get to the 'maybes' pile that they then might consider the 'late' applications?

I know this is my own fault. I am not looking for exceptions, just a reality check. I'm not looking for any judgement on my specific case, just the rough chances that my application is even looked at. I have been working on grad applications for months. I just overextended myself and (somehow) got mixed up on the date as consequence. I have other options, I will live, but the situation does feel a bit unfortunate.