A 3-year-old boy has developed a maculopapular rash after 3 days of fever and runny nose. What is the most likely diagnosis?

The presentation of fever and runny nose followed by the development of a maculopapular rash in a 3-year-old boy aligns closely with measles. Measles is characterized by a classic progression of symptoms beginning with a high fever, cough, conjunctivitis, and a runny nose, often referred to as the "three C's." The maculopapular rash typically appears a few days after the onset of the initial symptoms and starts on the face before spreading downward.

In contrast, chickenpox would present with an itchy vesicular rash that appears in crops, beginning with spots that evolve to blisters rather than a maculopapular rash. Rubella generally causes a milder illness, with a rash often appearing simultaneously with or shortly after the fever and without the preceding severe symptoms often seen with measles. Scarlet fever would be associated with a different presentation, including a sore throat and a characteristic "strawberry tongue," rather than the respiratory symptoms and rash sequence typical of measles.

The sequence of symptoms and the nature of the rash in this case strongly indicate measles as the most likely diagnosis.