this is usually stated as: the probability of your hypothesis (‘the die is weighted’) given your evidence (the rolls you’ve seen) is proportional to the probability of your evidence given your hypothesis (the odds you’d see those rolls if the die were weighted) times the probability of your hypothesis (how likely is the die to be weighted to begin

how we should adjust probabilities when we encounter new data,

Any Bayesian analysis begins with an initial belief, aka a prior. In our case, the prior was the initial guess we had about the location of the target ball. Then we encounter objective information, which in our case was whether the new ball landed to the left or the right of the target ball. When you combine the two it gives you the improved belief