Is it possible to calculate the probability of a child having an IQ in a certain range based on their parents' IQ? For instance, if two parents have IQs of 160, can one calculate the probability that their child has an IQ over 160?
This is precisely the question Galton had in mind when he invented regressions. He tested it with heights. Given parents heights, their children height is actually more likely to be closer to the population mean. So high parents tend to have smaller children, and short parents taller children (hence the term "regression"). To answer your question, a children of parents with high IQs (160 is very high), is likely to have a higher IQ than the average population, but lower than the parents. This is even more true than for height as IQ is a lot less heritable. The precise likelihood can be calculated given some assumption.

Galton, F. (1886). Regression towards mediocrity in hereditary stature. The Journal of the Anthropological Institute of Great Britain and Ireland, 15, 246-263.