Let's consider an example. I have patient level data, their symptoms, reading from various medical tests. Based on that, I have built a binary classifier given patient data to classify if they are likely to have a disease, and if so, I'd want to manually run medical tests on them. For that case, we look at the disease class and rank order the predicted probabilities and select the riskiest patients to have the disease.
A few months later, say the disease evolves into a different strain. So we already have an imbalanced class of healthy vs infected patients. Not the new strain will be still a smaller population. Apart from that, the symptoms, various test readings will also be different. So translating this to a multi-classification problem makes sense. When you build a multi-classifier, and you have three probabilities, how would you go about rank ordering the same set of patients?
If you're interested in the risk of patients likely to be infected, taking the max of the either of the strain of disease a good way to proceed or is there a method to choose them based on their individual probabilities?
Edit: To bring a little more clarity. The multi:softprob gives the probability for each of the classes. If you have three classes, it will give three probabilities for each class summing up to 1. More details are here.
Given that we will get multiple probabilities for each row/patient from the example above, how do you go about choosing the final probability to rank order risky patients.