How to compute probabilities from list of boosted trees in xgboost

If number of trees == num of boosting rounds
  score = sum over predicted leaf values over all trees + 0.5
  prob = exp(score)/(1+exp(score)) or 1/(1+exp(-score))

If number of trees == num of boosting rounds * number of class
  score_i for all class i  = sum over predicted leaf values over all trees + 0.5 , for all class i
  prob_i for i = exp(score_i)/sum_i_(exp(score_i))

References:

• https://stackoverflow.com/questions/39858916/xgboost-how-to-get-probabilities-of-class-from-xgb-dump-multisoftprob-objecti/40632862#40632862
• https://stackoverflow.com/questions/37193953/how-to-use-xgboost-r-tree-dump-to-compute-or-do-predictions?rq=1
• https://homes.cs.washington.edu/~tqchen/pdf/BoostedTree.pdf
• https://stackoverflow.com/questions/39858916/xgboost-how-to-get-probabilities-of-class-from-xgb-dump-multisoftprob-objecti
• https://stats.stackexchange.com/questions/245537/calculate-probabilities-from-xgb-dump-for-multisoftprob-objective-formula
• http://xgboost.readthedocs.io/en/latest/parameter.html
• https://www.youtube.com/watch?v=Vly8xGnNiWs