Here's a fun "conditional probability" example: Both vaccination rates and hospitalization/deaths are very left skewed, while the US population is right skewed. What effect does this have look at vaccine efficacy, but normalize by current hospitalizations, because you're a hack? 
Let's assume for simplicity the weighted average of vaccines is 90% effective, and also flat across age groups. Conditioned *only on dath/hospitalization*, 35% of all deaths will still be fully vaccinated individual, and 24% of hospitalizations will be vaccinated. Not great!
But considered relative to *the entire population*, while deaths are still split evenly between vaxxed and not, there's so many protected in the vulnerable group, the population deathrate dropped by a factor of 7. Consider that graph, with a 0% vaxxed population for comparison:
In other words, breathless stories about how "X% of people who had Bad Thing happen were vaccinated!!" tell you nothing about how effective vaccines are, because you would expect a large chunk of Bad Things to happen to the vaxxed because they're 5-10x the size of the others now.
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