How to turn linear regression into logistical regression I followed these articles to implement logistic regression. 

I'm confused however because after training the model and getting the weights for my variables I don't now how to use the one-hot vector to turn this into confidence scores for the different classes.

I've got the formula: y' = x1W1 + x2W2 + x3W3 + b

I've got values for all Ws and b.

I've got my one-hot vector: [[1, 0, 0], [0, 1, 0], [0, 0, 1]]

How do I combine all this into confidence for each class?
You should use softmax to convert your output in probabilities. For only two classes, you have the formula $P(x  \in class 1) = \frac{\exp(y_{\text{class1}})}{\exp(y_{\text{class1}}) + \exp(y_{\text{class2}})}$. It mentioned in your article.