ppm/K to ppm/°C formula
Kelvin and Celsius are the same scale, but Kelvin is shifted so zero lines up with absolute zero while Celsius is shifted so zero lines up with the freezing point of water, for convenience. The step size of both are the same.

It is like how km can be used to measure distance from my hometown instead of your hometown to the same location. The size of each km is the same, but your reference point is different.

The difference is 273.15 K or °C. So 0 °C is 273.15 K, but that is absolute temperature. A ppm/K or ppm/C is a relative measurement that only cares about changes in temperature and in that case the 273.15 term appears twice, once for K and once for °C so it subtracts itself out of the equation.