# In multinomial logistic regression, how to explain the softmax outputs properly?

I tried to solve multiclass problem ("cat", "dog", "horse") problem and figured out that the more words in test text, the more difference between classes.

I grouped the output by number of words and created bins, getting the mean values of probability scores for the classes:

                cat          dog      horse      n_words
(0, 5]      0.322369    0.319800    0.357831    3.392157
(5, 10]     0.293250    0.307544    0.399207    8.722892
(10, 15]    0.301972    0.306258    0.391769    13.076923
(15, 25]    0.254966    0.280201    0.464833    20.546961
(25, 35]    0.239433    0.261795    0.498772    30.387755
(35, 50]    0.176405    0.300194    0.523401    38.571429


Is there any mathematical explanation for this observation? Any sources to read are very welcome