title: Multinomial Logistic Regression get probabilities using model coefficients and intercepts
body: <p>I have a 5 class multinomial logistic regression <code>model = LogisticRegression(multi_class='multinomial', solver='lbfgs')</code>  using sklearn and I would like to achieve the same output as <code>model.predict_prob()</code> just using the coefficients and intercepts.</p>
  <pre><code># model.classes_
  array([1, 2, 3, 4, 5])
  
  # model.coef_
   array([[ 0.07011634, -0.01660448, -0.02280068, -0.0142022 , -0.02046682],
          [-0.0165452 ,  0.06987072, -0.00576749, -0.01930324, -0.01419374],
          [-0.01615717, -0.01411199,  0.07353034, -0.01734335, -0.01666161],
          [-0.01659975, -0.02089339, -0.01998879,  0.06762984, -0.02415484],
          [-0.02081421, -0.01826086, -0.02497338, -0.01678105,  0.07547701]])
     
  # model.intercept_
   array([ 0.10282811, -0.12500906, -0.0892085 ,  0.14219192, -0.03080247]))
  </code></pre>
  <p>For a given row</p>
  <p><code>X[0] = array([14.4429439 ,  9.89014464, 13.20301328, 14.79792498,  9.61442853])</code></p>
  <p>how can I get the probabilities of each class using the model <code>coef_</code> and <code>intercept_</code> to be the same as below?</p>
  <p><code>model.predict_proba([X[0]])</code></p>
  <pre><code>array([[0.24858766, 0.16423193, 0.2136478 , 0.23815396, 0.13537864]])
  </code></pre>