Non-volitional is a non voluntary conversion which is forced on someone. This usually means that the person is hostile to the belief they later come to hold, as it is forced it is not sought after either. God is usually involved by a direct action such as a voice or lights, which results in the conversion being sudden. The scale of these conversions are massive as they are dramatic and spectacular due to the intervening act by God.
An example of a non-volitional conversion is Saul / St Paul. Saul was well known before his sudden conversion for murdering anyone who followed the Lord, as he was hostile to the belief they held. As he was on his way to Damascus one day a dramatic and spectacular light fell from the sky and he heard a voice. This voice told him to go to the city, where he would be told what to do. When he arrived at the city a man came to him to cure his blindness caused by God's intervening act. The scale of Saul's change was massive, this is seen in the fact that he changed his name to St Paul and completely changed his life around by preaching and following the Lord, despite not seeking the conversion.
Volitional conversions however are looked/sought for usually because they have a sense of revulsion at their life, which means they are voluntary. As they are sought for they are usually gradual as it takes time to know what you are seeking, which results in the process happening over a long period time. Volitional conversions happen on a low key scale usually just within oneself, which represents a lesser change compared to on-volitional conversions.
Tolstoy's conversion is one of the more well-known volitional...