When your nose is congested it generally means there is waste that needed to be removed, and is being removed (via the sinuses). You may find them runny when there isn't too much mucous - as you have just fasted, and that may minimise the thick mucous in the nose - making it thinner. This can easily come out when you tilt your head down.
Sometimes my nose gets really blocked, and I can't even "sniff" which lets any nose dribble fall out.... Hope this helps somewhat? Take care