Classify dataframe rows based on probabibility

I have two dataframes. First one is related to users and looks like this:

user_id    city_id
  0           a
  1           a
  2           b
  3           a
  4           c
.. and so on

Second one gives information how many percent of each city belongs to each district, something like this:

 city_id     district_id    probability
    a             a1           0.01
    a             a2           0.02
    a             a3           0.02
    a             a4           0.56
    a             a5           0.39
    b             b1           0.63
    b             b2           0.07
    b             b3           0.30
 and so on.. 

I need to organize users based on this probability to which district of their city they belong. So (for example) that I get approximatelly 56% that users that live in city a are from district a4 and so on. Basically final df would have rows related to the user_id, city_id and district_id.

My first clue was to give each user a random number and to compare with the probability.

My second idea was to group by rows by city_id, to look up at the second table and select (give value to the third column) by probability. So basically for the city a, that means that I will select 56% rows in the group and give it district value a4 and so on. But I am not sure that mathematically is the best way.