I am not clear which probability you want.

Scenario A: The lottery runs once a week. A person plays one week and wins. S/he does not play for a few weeks, then plays again and wins again. Once more, s/he does not play for a few weeks, then plays again and wins again. So the person wins three times and plays only three times.

Scenario B: The lottery runs once a week. A person plays every week. After winning the first time, the person continues to play each week, and wins again after not winning several times, and then winning for the third time after again not winning several times. So the person wins three times but plays more than three times.

Which of these scenarios do you mean? Or do you mean something else altogether?