Understanding the softmax algorithm

So I am learning about machine learning. One of the excercises I did was essentially run the softmax algorithm on a list of values to compute the respective probability of each. It took a little bit of time, but I eventually found a python example and reverse-understood it. I am going to give a list of numbers and show how to run the softmax on them.

Take the set
[3.0, 1.0, 0.2]
To compute the softmax values, first find e^(x), where x is each element in the set.


These numbers are approximate, of course. Let’s put these new numbers in another set
[20.08553692, 2.718281828, 1.221402758]

Now, to find the softmax values for each, simply divide each element by the sum of elements in the set

20.08553692 / 24.02522151 = 0.836018803
2.718281828 / 24.02522151 = 0.113142841
1.221402758 / 24.02522151 = 0.050838356

To test, one can add up the softmax values and make sure they add up to be 1

0.836018803 + 0.113142841 + 0.050838356 = 1