It seems like my knowledge (confidence in my probability assessment) of the shape of a distribution is continuous

You are right. Knightian uncertainty isn't a separate discrete category, it's an endpoint of a particular interval on the other end of which sits uncertainty that you know everything about, e.g. the probability of drawing a red ball from an urn into which you have just placed 10 red and 10 black balls.

Knight himself called known uncertainty "risk" and unknown uncertainty "uncertainty". He wrote: Uncertainty must be taken in a sense radically distinct from the familiar notion of Risk, from which it has never been properly separated.... The essential fact is that 'risk' means in some cases a quantity susceptible of measurement, while at other times it is something distinctly not of this character; and there are far-reaching and crucial differences in the bearings of the phenomena depending on which of the two is really present and operating.... It will appear that a measurable uncertainty, or 'risk' proper, as we shall use the term, is so far different from an unmeasurable one that it is not in effect an uncertainty at all."