Comment by wfunction

+1 it was actually a rather horrifying presentation of Bayes's theorem. I would just explain it in 2 lines:

P(Cause and Effect) = P(Cause) × P(Effect given Cause) = P(Effect) × P(Cause given Effect)

so P(Cause) = P(Effect) × P(Cause given Effect) ÷ P(Effect given Cause)