90% sounded high; I found an article saying as of today 79% of people in France have had both of the initial shots (not sure how they figure single-dose vaccines like J&J and Oxford), and 80% had 1. [1]

Let's say it's 80%. 80/20. Primary vax status probably hasn't changed too dramatically in 1 month.

p(hospitalized | vaxxed) = p(vaxxed | hospitalized) * p(hospitalized) / p(vaxxed)

= 0.6 * p(hospitalized) / 0.80

= 0.75 * p(hospitalized)

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p (hospitalized | unvaxxed) = p (unvaxxed | hospitalized) * p(hospitalized) / p(unvaxxed)

= 0.4 * p(hospitalized) / 0.2

= 2 * p(hospitalized)

Vaccination gives a 2.67x reduction in hospitalizations (against omicron which all the anti-vaxxers are saying the vaccines don't do anything against).

With your 90% figure, it becomes 2/3 instead of 3/4 and 4 instead of 2, which is 6x, confirming what the other replier got.

[1] https://www.sortiraparis.com/news/coronavirus/articles/23973...