With Covid, many of the vaccines target a highly functional portion of the virus for the induced immunity. This means that mutations that make the vaccine induced antibodies less effective are at least somewhat likely to alter the function of the virus.
My understanding is that we aren't really able to analytically determine the possibility space.
That's only true if the vaccine stops almost all infections, which the COVID vaccines do not.
There's another comment in this thread from someone who's been vaccinated and sick for 9 days. That's a great environment for the virus to evolve immunity to the vaccine. And it's not an uncommon situation.
Again, like the person above you said, it's not that simple. Bacteria can develop resistance to antibiotics because they can either avoid or start to digest the chemical that would normally be harmful to them. Here it's not the vaccine that's killing the virus - it's your own immune system, and every single one is different. So yeah, maybe in this person's body the immune system didn't learn to recognize the virus and kill it - it means literally nothing for how another person's immune system will behave when they encounter it.
Vaccinations teach everyone's immune system to target the same part of the virus. Since everyone has immunity to the same spike protein, a change in that protein means something to all vaccinated people.
It’s a long story, but part of the reason is that bacteria evolve resistance in the presence of the antibiotic, while here, the virus would need to randomly evolve it in the unvaccinated, then sustain useless adaption for a while until it gets the opportunity to infect a vaccinated person.