Model to predict based on frequency of occurrence
For something like this, you could go with a simpler approach. One idea is to sample randomly among the cities that a given passenger has visited using the amount of times each city has been visited as probabilites.

Here's a way you could do so. I've added a few more examples to the dataframe so that the application is seen more clearly. Say you instead have:

     Passenger    Trip
0       John     London
1       Jack     Girona
2       Jack      Paris
3        Joe     Sydney
4        Joe  Amsterdam
5        Joe  Barcelona
6        Joe  Barcelona
7       John     London
8       John      Paris
9       Jill    Newyork
10       Jim     Sydney
11      Jack      Paris
12     James     Sydney


You could define a function like the folllowing in order to randomly sample from the existing data in the dataframe:

def random_sample(df, name):
    import numpy as np
    # group the dataframe by Passenger and count 
    # the different trips 
    g = df.groupby('Passenger').Trip.value_counts()
    # Make the probabilities add up to 1
    freq = g[name] / g[name].sum()
    # random destination based on 
    # its probabilities
    random_name = np.random.choice(a=freq.index, size=1, 
                     p = freq.values)[0]
    # return likelyhood of next randomly chosen
    # destination and destination
    return freq[random_name], random_name




 Usage

Say we want to select a a randomly samples destination for say Joe and also to know which is the likelihood. Considering that the destinations where Joe has been are:

Trip
Barcelona    2
Amsterdam    1
Sydney       1


We could get for example:

for _ in range(5):
    freq, dest = random_sample(df, 'Joe')
    print('Chosen destination {} with a probability of {}'.format(dest, freq))

Chosen destination Sydney with a probability of 0.25
Chosen destination Barcelona with a probability of 0.5
Chosen destination Barcelona with a probability of 0.5
Chosen destination Barcelona with a probability of 0.5
Chosen destination Sydney with a probability of 0.25