[j7ake]

It's unfortunate the first equation was mistyped, one way to check is that the Bayes's rule can be derived from a rule in conditional probability:

P(A,B) = P(B,A)

P(A|B) * P(B) = P(B|A) * P(A)

The formulation in the blog post would say instead:

P(A|B) * P(A) = P(B|A) * P(B)

which does not really make sense.