I agree that conditional probability is best demonstrated graphically. The sample space is a big rectangle, and events are represented as polygons or other closed shapes, with area proportional to their probability. Conditional probability elegantly falls out of this representation by treating one of these event-shapes as a new "sub sample space" and computing fractions of areas.

So this area model at once creates a lot of confusion elsewhere.

Then you can blow your students' minds with the possibility that the "rectangle" is actually the unknowably massive timeline of the entire universe, from the Big Bang until its heat death, and all of our models and reasoning are conditional on some subset of that gigantic world-rectangle. In my opinion, the power of this philosophical leap is lost without the basic geometric intuition.

Think about it like PCA. Do you lose some information? Yes. But you can do a lot with only the first few principle components (i.e. basic concepts).

Things like events, sets, measures, etc add important details like why you have to divide the selected row / column by its sum to get a true conditional distribution; how many dimensions the array should have; constraints, properties, and relationships of subarrays, etc. But that all becomes a lot easier to understand once you have the basic intuition. And once you get good enough you can start to let go of the grounding in arrays and ground in other concepts and then think about it more abstractly.