When water is cooled from [tex]40^{0}C[/tex] to [tex]0^{0}C[/tex], the temperature of the solution is decreases. Due to decrease in temperature, the intermolecular forces which are present between the solute particles will not break easily.
Decrease in temperature also results in the decrease in solubility. Thus, due to decrease in temperature, [tex]KNO_{3}[/tex] will precipitate implies that the solubility of [tex]KNO_{3}[/tex] in water decreases.
Hence, precipitation of [tex]KNO_{3}[/tex] occurs.