Generally, normalization allows features of different natures to be used meaningfully together. Without it, features would impact the KNN functions proportionately to the magnitude of the numbers that are used to express them. E.g. GDP per capita would cause unemployment rate to be nearly irrelevant without normalization.
In dealing with distance, all features would share a common "unit" already and are correctly scaled relative to each other, so normalization would not be needed in this instance.