In science we believe
Belief in science is likely partly based on scientists’ ability to predict.
As M.S. notes, climate scientists accurately predicted that temperatures were going to rise in the future in late 1980s. Hence, for people who are aware of that (like himself), belief in climate science is greater.
Similarly, unpredictability in weather (as opposed to climate), e.g., snowstorms, which are typically widely covered in media, etc., may lower people’s belief in climate science.
Possibility of showers in the afternoon
Over conversations with lay and not to say lay people, I have observed that sometimes people conflate probability and possibility. In particular, they typically over-weight the probability of a possible event and then use that inflated weight to form the judgment. When I ask them to assign a probability to the event they identify as a possibility, they almost always assign very low probabilities, and their opinion comes to better reflect this realization.
Think of it like this: a possibility for people, once raised (by them or others) is very real. Only consciously thinking about the probability of that possibility allows them to get out of funky thinking.
Something else to note. Politicians use ‘possibility’ as a persuasion tool, e.g., ‘there is a possibility of a terror attack’ etc. This is something I have dealt with before but I leave the task of where to people motivated to pursue the topic.