Hm, I think perhaps I overcomplicated the situation.
Instead of Bayes' theorem I just use the formula for conditional probability which says that I am supposed to find:
P((A∩B)∩(three events occur)) / P(three events occur))
Thus, I get (0,4*0,8*(three events)) / (three events)
(Note: this is because the events are classified as independent, in which case P(A ∩B) = P(A)*P(B)
The probabilities related to three events cancel each other out, and thus I am left with 0,4*0,8 = 0,32.
Is this correct?