Philosopher Marc Lange gives an overview (pdf) of the debate on Hume's Problem of induction. Chapter 9 (starting on p. 80) is called "Bayesian approaches". I understand it as: the justification for induction might be updating believes from a Bayesian point of view. Lange continues with a fictional dialogue between a Bayesian (B) and an inductive skeptic (S). I summarize:

B: if you admit Bayesian approaches are valid, what kind of prior do you suggest, which fundamentally makes updating believes a non-justification of induction.

S: any distribution with "no degree of confidence to which we are entitled regarding predictions regarding unexamined cases" (Lange), where "no degree of confidence" does not mean the value zero but no value at all [e.g. a NULL in the R language].

B: this prior violates probability axioms - it is not a distribution [and not implementable in R either].

My questions are:

Does B's last claim reflect the working Bayesian's position?

Can the skeptic S consistently defend her skeptical position still including the acceptance of Bayesian techniques by her construction of a prior distribution?