# Multiclass imbalanced classification

I have a dataset with the target variable having 3 classes. Value counts of Target variable are as follows:

Class A :26000
Class B: 5000
Class C: 500
Class C  prediction is most important from a business standpoint.


To date I have mostly done binary class (mostly 1:0.12) distribution of target class,wherein at the end, deciling of prediction probabilities is done, in decreasing order of probabilities starting with D1 as the highest probability and D2 the lowest.

Now with influx of a new class that too with so less population,I am perplexed on three aspects.

What algorithms are best? What metric should be used? How to get a deciling of probabilities in this case, if applicable?