Those 3% are not cases of “you might get it if unlucky”, but cases of “failed to generate an strong enough immune response which leads to the formation of T-Memory Cells”. So if you are in those “3%”, the outcome of infection will be the same as in a person who is not vaccinated. That’s one more reason why everyone who can should get the vaccine - to protect those who got the vaccine and are still vulnerable.

The targeted immune system takes a few days to create the right antibodies for a specific target, because antibodies are not made-to-fit, they are generated randomly until something sticks (quite literally). Those days are the difference between “virus infection gets crushed instantly” and “virus has enough time to replicate in unmanageable numbers”. If you have Memory Cells, the immune system can “fast-forward” and can just skip to the fun part.