Predicting probability of occurrence using Historical Time Series Data
Without having more context this is how I would approach this -
Assuming there is not meaning to being 'close' in the prediction. I.E, if real 1001 number was 42, then predicting 41 and 99 is just as wrong.
If we assume no stochastic structure to the series, I.E previous number dosnt affect current number I would use the top 5 most frequent numbers as predictions.
If we assume there is a stochastic structure to the series, under our assumption that difference between numbers is not a factor. We can treat this problem as a sequence prediction problem. This is common in text analysis and there are various models that can be used.
Assuming there is a meaning of being 'close' to the prediction.
IF no stochastic nature, use the 5 percentiles based on 1000 values series as predictions.
If yes stochastic nature, use time series modelling. AR(IMA) modelling perhaps.