For aviation purposes, a ceiling is the lowest broken or overcast cloud layer that is forecast to be present. A broken ceiling will be forecast if the sky is expected to have cloud coverage over 5/8 to 7/8 of the sky, and the sky is expected to be overcast when clouds will cover 8/8 of the sky.
If the ceiling is listed as "None," that does not mean there will not be clouds in the sky. It only means that clouds will not cover more than half (4/8) of the sky.
If precipitation is in the forecast and the ceiling is listed as "None," then expect clouds to be present (Clouds are needed for precipitation) but covering less than half of the sky.
Image 1. The daily forecast showing the ceiling as "None." There is precipitation in the forecast.