Unlike Jack, I'm pessimistic about your proposal. I've already changed my mind not once but twice.

The interesting aspect is that this doesn't feel like I'm vacillating. I have gone from relying on a vague and unreliable intuition in favor of 1/3 qualified with "it depends", to being moderately certain that 1/2 was unambiguously correct, to having worked out how I was allocating all of the probability mass in the original problem and getting back 1/3 as the answer that I cannot help but think is correct. That, plus the meta-observation that no-one, including people I've asked directly (including yourself), has a rebuttal to my construction of the table, is leaving me with a higher degree of confidence than I previously had in 1/3.

It now feels as if I'm justified to ignore pretty much any argument which is "merely" a verbal appeal to one intuition or the other. Either my formalization corresponds to the problem as verbally stated or it doesn't; either my math is correct or it isn't. "Here I stand, I can no other" - at least until someone shows me my mistake.