Q:

random forest in python: final probabilities in classification problems

In classification problems  a RF classifier give the final response according to majority voting, e.g. yes or not about an event.
On the other hand in Python I can see also a vector with the final probabilities of the event, e.g. 0,83. how this probability is calculated if I have 1000 estimators, is the mean of 1000 probabilities, from each tree?
clf = RandomForestClassifier(max_depth = 4, min_samples_split=2, n_estimators = 200, random_state = 1) 
clf.fit(train[columns], train["churn"]) 
predictions = clf.predict(test[columns]) 
predicted_probs = clf.predict_proba(test[columns]) 
print(predicted_probs) 
test = pd.concat([test, pd.DataFrame(predicted_probs, columns=['Col_0', 'Col_1'])], axis=1) 

A:

is the mean of 1000 probabilities, from each tree?

Yes, it is. 

The vector shows the average probability of each selected class across all the trees. The final voting in Scikit RF classification selects the class with the highest mean probability for a given input for all trees.
So if for a dual class dataset, C1 and C2 have probabilities 0.3, 0.7 and 0.5, 0.5 across trees labeled 1 and 2 respectively for a given sample/input. C1 has an average probability of 0.4 while C2 an avg. of 0.6. 
C2 is the selected class for that input as it has the highest mean probability across both trees.

You can also take a look at the source for the predict method of ForestClassifiers. From the __doc__ of the method:

The predicted class of an input sample is a vote by the trees in
  the forest, weighted by their probability estimates. That is,
  the predicted class is the one with highest mean probability
  estimate across the trees.

Summarily, it's a type of majority voting where voting weights are not class frequencies across trees but mean values across trees.

