A truncated version of Bayes used here:

A=Infantile botulism

B=Kid eats honey

P(A|!B) = P(A) * (1 - P(B|A))

Not sure it is correct!

The ACX signature says:

P(A|B) = [P(A)*P(B|A)]/P(B)

So

P(A|!B) = [P(A)*P(!B|A)]/P(!B)

= (1/40000) * .8 / ???

??? Is very small though if people take the medical advice.

Their number assumes nobody follows the advice!