If you don’t think the concept of “objective probability” is salvageable I agree that you wouldn’t want to use it for defining other things.
I don’t want to go into detail of my personal account of objective probability here, not least because I haven’t spent enough time working it out to be happy it works! The short answer to your question is you need to define an objective measure over possible observers. For the purposes of defining existential risk, you might be better to stop worrying about the word “objective” and just imagine I’m talking about the subjective probabilities assigned by an external observer who is well-informed but not perfectly informed.
If you don’t think the concept of “objective probability” is salvageable I agree that you wouldn’t want to use it for defining other things.
I don’t want to go into detail of my personal account of objective probability here, not least because I haven’t spent enough time working it out to be happy it works! The short answer to your question is you need to define an objective measure over possible observers. For the purposes of defining existential risk, you might be better to stop worrying about the word “objective” and just imagine I’m talking about the subjective probabilities assigned by an external observer who is well-informed but not perfectly informed.