How to measure/weight the importance of tags? Lets say we have $T$ tags and $N$ articles and lets say that for each tag $t_{i}$ we know that it has tagged $n_{i}$ articles. Meaning that, frequency($t_{i}$)=$n_{i}$.
Given the above information how could I compute the probability P($t_{i}$ to tag a new article) or more generally how could I go about scoring the "importance" of each tag in Tag set ?
 A: I am not absolutely sure what you want to achieve but I will give it a try.
Measuring Importance
The concept of importance without any target is rather ambiguous. Suppose you have the tags "football","crops" and "funny". Now want to create a classification algorithm to determine whether a certain article is in the category "agriculture" or "sport". In this case the tags "football" and "crops" are more important than "funny". On the other hand, if you want to classify documents whether they are funny or not, "football" and "crops" maybe less helpful. I think you get the idea.
Sooo ... in relation to a certain label, you can measure the importance of tags by calculating the information gain ratio or related measures.
Calculating a probability
Without such a target, you can "only" calculate the probability that a certain tags occurs. In detail: You can calculate this probability either a priori (|Tag=ti|/|tags|) or a posteriori, i.e. the probability that a given article is tagged with a certain tag ti (prob(Tag=ti|Article=art)). 
The latter can be achieved by constructing a bayes model (e.g. naive bayes) for each tag. In this case a binary label is constructed with value "1" if the tag is present, else "0".
A: First for calculating the importance of each tag in a new article I would use the bag of words format to store the corpus information plus the new article added to the last row. I would calculate the tf-idf of the sparse matrix containing the rows with articles and the columns with words. Then I would just Keep the columnns with the tags. Then I would get the tf-idf values of the new article tags, add them all in order to get the total, an to calculate the probability of each one I would divide the tf-idf of the tag from the last article cell divided the calculated total and multiply it by 100. This will provide me the percentage that each tag represents from the article.
For calculating the importance of a tag in a tag-set I would add all the tag columns. From those totals I would add them all and get the grand total. Then I would take each tag divide it for the grand total and multiply it by 100. This will provide me with the percentage or total importance of each tag.  
