Prediction of n class variables I have a historical data that has discrete variables.
 Let say I have data points with class labels   
1, 2, 3, 4, and 5

For a given classification problem, I can use the training data and then get the trained model. Using the trained model, I can classify the labels. However, I am also interested in prediction of class labels. 
My requirement is that for a given $N$ points, lets say 5 data points, I want to know what is the probability that class label 5 more likely or less likely occurs from 0 to 1. Can anyone give me any ideas on this? For example my output will be a prediction probability for 5 instances, being: 
0, 0.1, 0.2, 0.3, 0.5. 
This means that the first data point has zero probability for class label 5 to occur. The 5th data point has the highest probability to occur around 50%. Can anyone give me idea on how to go about this problem?
 A: First let me rephrase the problem to make sure I understand it: you have 5 points, but you don't want to classify the points, you want classification probabilities.
If that's the case, that's what multinomial regression (Wikipedia) is designed to do. It's covered in several textbooks; I learned out of Categorical Data Analysis (Amazon link to 3e)  by Agresti but it might not be the best book for self-study.
You can also use a neural network (blog post by Brian Dolhansky) that outputs class membership probabilities. Interesting coverage of the subject here (Ou and Murphey, 2007, Multi-class pattern classification using neural networks. Pattern Recognition 40, 4-18).
A: Not sure i understand what you are asking... You can determine the probability of getting class label 5 btwn 0 and 1 by simply adding the probability of getting 5 @ 0 & prob of getting 5 @ 1 (p(0) + p(1) = 0 + .1 = .1)
Solution: Since Prob of getting class 5 btwn 2 & 4 would be--> p(2) + p(3) + p(4) = .2 + .3 + .5 = .9 & prob of 5 btwn 0 & 1 = p(0) + p(1) = 0 + .1 = .1
.9 > .1 Thus Class label 5 is less likely to be btwn 0 & 1.
