what interpretation of the word "probability" does allow you to think that the probability of something is 1 and then change to something other than 1?

They need to have inconsistent attitudes about how they calculate probability, or estimate probabilities by inherently irrational means such as assigning likelyhood based on what hypothesis they want to be true the most and acting like that belief is certain. Empirically, I've met individuals who claim that no amount of evidence would alter some of their beliefs so something like this may be going on. It is however possible that trying to model these beliefs as probabilities implies a degree of rationality that they simply lack. The human mind is not generally a good Bayesian.

what interpretation of the word "probability" does allow you to think that the probability of something is 1 and then change to something other than 1?

Any interpretation where you can fix a broken model. I can imagine a conversation like this...

Prankster: I'm holding a die behind my back. If I roll it, what probability would you assign to a 1 coming up?

cupholder: Is it loaded?

Prankster: No.

cupholder: Are you throwing it in a funny way, like in one of those machines that throws it so it's really likely to come up a 6 or something?

Prankster: No, no funny tricks here. Just rolling it normally.

cupholder: Then you've got a 1/6 probability of rolling a 1.

Prankster: And what about rolling a 2?

cupholder: Well, the same.

Prankster: And so on for all the other numbers, right?

cupholder: Sure.

Prankster: So you assign a probability of 1 to a number between 1 and 6 coming up?

cupholder: Yeah.

Prankster: Surprise! It's 20-sided!

cupholder: Huh. I'd better change my estimate from 1 to 6/20.

Sure, I was simply referring to the isolated quote in question: comment that Normal_Anomaly was replying to had a lot of problems, but I don't think that the sentence in question was the one that deserved criticism.