Did is correct that P(_|A) can be treated as a probability function. It's what you get by starting with a probability function P and then revising it by conditionalizing on A (= learning that A is definitely true). So that's not an issue. The Lewis result is also not about zero-measure events, although they do come up eventually if you really dig into this topic.
I just updated the Wiki article (written by me a number of years ago) to read:
...only certain trivial Boolean algebras with very few elements contain, for any given A and B, an event X such that P(X) = P(B|A) is true for any probability function P.
In other words, in general there's no single event X, fixed by the choice of A and B, such that P(X) tracks P(B|A) as we vary the probability function. That's the Lewis result, also referenced in the Wiki article on Causal Decision Theory.
I think Lewis's result can be visualized as follows. Imagine a square pool with a flat bottom. We can make waves as big as we like, so the water surface is by no means flat. But the total volume is of course constant, and is equal to 1 (that is, 1 pool's worth).
We can draw Venn diagrams on the flat bottom, to represent events. The volume of water above circle A corresponds to the probability of event A. Because the water can slosh around, a fixed circle can have varying probabilities.
The conditional probability P(B given A) is a ratio: the volume above the intersection of A and B, divided by the volume above A. Lewis is saying that there's no circle (or other fancy shape) that you can draw, anywhere on the bottom, that will reliably have a volume above it numerically equal to that ratio. Draw any circle you like, you will always have the ability to move water around so that the volume above that circle is different from the ratio of the A-and-B volume to the A-volume.
The nonstandard domains used for conditional event algebras would then, by analogy, begin with an idea such as "Imagine that every circle A there's a matching pool, suspended in the air above it..." Just to convey the flavor.
What are conditional events? If you're drawing balls from an urn, a conditional event would be something like "If the third ball is red, the fourth ball is blue." When we treat the if-then as a material conditional (that is, "If A then B" being equivalent to "Either B or not-A"), then the event in question occurs if the third ball is something other than red. Whereas proponents of conditional event algebras would say the event cannot be judged to have happened or failed to happen until the condition "third ball red" is met.
Lewis didn't (that I'm aware) have anything to do with developing conditional event algebras, except to produce this finding which prompted others to explore ways of getting around it.