According to Bayesian inference/confirmation theory, your confidence in a hypothesis increases as you observe more and more evidence predicted by that hypothesis (according to bayes theorem and the laws of the probability calculus). These updates happen in a very specific way. Although there are some other problems associated with this version of confirmation theory, this is at least in principle quite intuitive.
However, in the face of a grue hypothesis, this idea falls apart. I could suggest some hypothesis "All A's are B's". Every time there is a new instance of an A being a B, my confidence in that hypothesis improves. However, we can form a grue-like hypothesis: "All A's are B's until time t". This hypothesis predicts the same thing as the former but there is a divergence at some arbitrary time as to what really happens.
Does our confidence in these two hypotheses really increase in the same way?
Is there any way to solve this problem which doesn't amount to arbitrary selection of prior probabilities to favour the former type of hypothesis?