I don't want to get into the swamp of discussing the philosophy of uncertainty/probability (I think it's much more complicated than "it's all in your head"), so let's try another tack.

Let me divide the probabilities in any particular situation into two classes: immutable and mutable.

Immutable probabilities are the ones you can't change. Note that "immutable" here implies "in this particular context", so it's a local and maybe temporary immutability. Mutable ones are those you can change.

Both of these you may or may not know precisely and if not, you can generate estimates.

In your lesion example, the probability for a person to get cancer is immutable. You may get a better estimate of what it is, but you can't change it -- it is determined by the presence or the absence of the lesion and you can't do anything about that lesion.

Imagine two parallel universes where you looked at a "random person", say, Alice, from your scenario. You ask her if she smokes. In universe A she says "Yes", so your estimate of the probability of her getting cancer is now 85.55%. In universe B she says "None of your business", so your estimate is still 45.5%.

Your estimates are quite different, and yet in both universes Alice's chances of getting cancer are the same -- because you improving your estimates did nothing to the physical world. The probability of her getting cancer is immutable, even when your estimate changes.

Compare this to the situation where you introduce a surgeon into your example. The surgeon can remove the lesion and after that operation the people with removed lesion are just like the people who never had it in the first place: they are unlikely to both get cancer and to smoke. For the surgeon the probability of getting cancer is mutable: he can actually affect it.

Let's say the surgeon operates on Alice, his initial probability is 45.5%, after he opens her up and discovers the lesion it becomes 90% (but the actual probability of Alice getting cancer hasn't changed yet!), and once he removes it, the probability become 1%. That's an intervention -- changing not just the estimate, but the actual underlying probability. Alice's actual probability used to be 90% and now is 1%. For the surgeon it's mutable.