The mental model theory was initially created to describe the comprehension of discourse and deductive reasoning. But, it can also describe naive probabilistic reasoning. I might write something about this later, but it will probably be a while. I think that I should read this book first if I did. I didn't go into any of the details of this in the above post. There are few other principles and it gets a bit more complicated. You can see this paper if you are interested.

A mental model is defined as a representation of a possibility that has a structure and content that captures what is common to the different ways in which the possibility might occur. It is a theory about how people naively reason, not neccesarily how they have been trained to reason which will probably be more explicit.

Here is an example:

According to a population screening, 4 out of 10 people have the disease, 3 out of 4 people with the disease have the symptom, and 2 out of the 6 people without the disease have the symptom. A person selected at random has the symptom. What's the probability that this person has the disease?

The model theory allows that probabilities can be represented in models and that the assertion can be represented by either a model of equiprobable possibilities or a model with numerical tags on the possibilities. This tag might be frequencies or probabilities. This means that people might make the follow models.

or an equivalent one if they are thinking in probabilities is

Ace is not more probable.

Ace is more probable in the scenario that I described.

Of course, as you say, Ace is impossible in the scenario that you described (under its intended reading). The scenario that I described is a different one, one in which Ace is most probable. Nonetheless, I expect that someone not trained to do otherwise would likely misinterpret your original scenario as equivalent to mine. Thus, their wrong answer would, in that sense, be the right answer to the wrong question.

I think the problem here is that you're talking to people who have been trained to think in terms of probabilities and probability trees, and furthermore, asking "what is more likely" automatically primes people to think in terms of a probability tree.

The way I originally thought about this was:

• Suppose premise 1 is true. Then two possible combinations out of three might contain a king, so 2/3 probability for a king, and since I guess we're supposed to assume that premise 1 has a 50% probability, then that means a king has a 2/6 = 1/3 probability overall. By the same logic, ace has a 2/3 probability in this branch, for a 1/3 probability overall.
• Now suppose that premise 2 is true. By the same logic as above, this branch contributes an additional 1/3 to the ace's probability mass. But this branch has no king, so the king acquires no probability mass.
• Thus the chance of an ace is 2/3 and the chance of a king is 1/3.

In other words, I interpreted the "only one of the following premises is true" as "each of these two premises has a 50% probability", to a large extent because the question of likeliness primed me to think in terms of probability trees, not logical possibilities.

Arguably, more careful thought would have suggested that possibly I shouldn't think of this as a probability tree, since you never specified the relative probabilities of the premises, and giving them some relative probability was necessary for building the probability tree. On the other hand, in informal probability puzzles, it's often common to assume that if we're picking one option out of a set of N options, then each option has a probability of 1/N unless otherwise stated. Thus, this wording is ambiguous.

In one sense, me interpreting the problem in these terms could be taken to support the claims of model theory - after all, I was focusing on only one possible model at a time, and failed to properly consider their conjunction. But on the other hand, it's also known that people tend to interpret things in the framework they've been taught to interpret them, and to use the context to guide their choice of the appropriate framework in the case of ambiguous wording. Here the context was the use of word of the "likely", guiding the choice towards the probability tree framework. So I would claim that this example alone isn't sufficient to distinguish between whether a person reading it gives the incorrect answer because of the predictions of model theory alone, or whether because the person misinterpreted the intent of the wording.