I read "Thinking, Fast and Slow" and some of the other references in the article. I found Kahneman's arguments persuasive, however the article makes me re-evaluate those conclusions.
When asked what is more probable, I think in terms of statistical probabilities. However the article makes an interesting argument that most people don't define the term, "more probable" the same way. I'm not convinced Kahneman was wrong, but I do see how simple changes in the wording of a question can lead to a material difference in answers. I also see that my own interpretation regarding the "correct" meaning of words aligned with Kahneman, and contributed to my general agreement with his conclusions.
Probabilities are a philosophical rat's nest of sorts. When it comes to statistics, it's generally agreed that we're working with a frequentist interpretation of the meaning of probabilities, but you are right that a person with no prior background could well have a completely different understanding here (subjectivist probability, degrees of belief).
I also think stating presuppositions and limitations around observation and prior knowledge is monumentally important as soon as you begin talking in terms of probabilities, if you really want your statements to be clear, but most people don't do this. There are some ways in which I think the casual use of probabilities can actually be more harmful than encouraging a simple binary boolean dichotomy of "I know" or "I don't know" and need more information.
Kahnemann had the intellectual honesty to accept that large parts of his book are flawed, and he called on psychologists to clean up their act by doing a systematic multiple reproduction study program:
https://www.nature.com/news/polopoly_fs/7.6716.1349271308!/s...