Regarding this question and its highest-voted answer: Conditional probability intuition.
So I get the idea of using Venn-Diagrams and limiting our "universe" to a new subset, but what happens if we try looking at it with a tree diagram?
Using this equation: $$P(A\vert B)P(B)=P(B\vert A)P(A)$$ we can set the probabilities to whatever we'd like, for example let's say $P(A)=\dfrac12$, $P(B)=\dfrac13$, $P(A|B)=\dfrac14$, $P(B|A)=\dfrac15$.
The equation does not hold, the events are dependent on each other.
If sequence of occurrence does matter, how can you continue using a Venn-Diagram to prove this equality?