Prior and Posterior probability

UserID LabelID Prior Likelihood Posterior
1 1 71/206 15/71 .07
1 2 27/206 2/27 .009
1 3 108/206 1/108 .004
2 1 71/206 21/71 .101
2 2 27/206 15/27 .07
2 3 108/206 7/108 .03
3 1 71/206 35/71 .169
3 2 27/206 0/27 0
3 3 108/206 100/108 .485
4 1 71/206 0/71 0
4 2 27/206 10/27 .04
4 3 108/206 0/108 0

Posterior = Prior * Likehood(category)
71/206 * 15/71 == .07

in reference to: How I Would Use the Google Prediction API ( To Find Your Musical Profile) | The Data Scientist (view on Google Sidewiki)