Markov transition matrix in Python

Markov_transition.py

#the following code takes a list such as
#[1,1,2,6,8,5,5,7,8,8,1,1,4,5,5,0,0,0,1,1,4,4,5,1,3,3,4,5,4,1,1]
#with states labeled as successive integers starting with 0
#and returns a transition matrix, M,
#where M[i][j] is the probability of transitioning from i to j

def transition_matrix(transitions):
    n = 1+ max(transitions) #number of states

    M = [[0]*n for _ in range(n)]

    for (i,j) in zip(transitions,transitions[1:]):
        M[i][j] += 1

    #now convert to probabilities:
    for row in M:
        s = sum(row)
        if s > 0:
            row[:] = [f/s for f in row]
    return M

#test:

t = [1,1,2,6,8,5,5,7,8,8,1,1,4,5,5,0,0,0,1,1,4,4,5,1,3,3,4,5,4,1,1]
m = transition_matrix(t)
for row in m: print(' '.join('{0:.2f}'.format(x) for x in row))

#0.67 0.33 0.00 0.00 0.00 0.00 0.00 0.00 0.00
#0.00 0.50 0.12 0.12 0.25 0.00 0.00 0.00 0.00
#0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00
#0.00 0.00 0.00 0.50 0.50 0.00 0.00 0.00 0.00
#0.00 0.20 0.00 0.00 0.20 0.60 0.00 0.00 0.00
#0.17 0.17 0.00 0.00 0.17 0.33 0.00 0.17 0.00
#0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00
#0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00
#0.00 0.33 0.00 0.00 0.00 0.33 0.00 0.00 0.33