Why the probability greater than 100% when I use Naive Bayesian for classification I use Naive Bayesian to train a dataSet:
weather     temperature humidity    windspeed   Y/N?

rain        cool        normal      strong      N
sunny       hot         high        strong      N
sunny       hot         high        weak        N
sunny       mild        high        weak        N
sunny       cool        normal      weak        Y
overcast    hot         normal      weak        Y
rain        mild        normal      weak        Y
rain        cool        normal      weak        Y
overcast    hot         high        weak        Y
sunny       mild        normal      strong      Y
overcast    mild        high        strong      Y

Table for count:

count(Y) = 7,count(N) = 4

Table for probability:

P(Y)=7/11, P(N)=4/11

Now, there is a new data:
overcast  hot   normal   weak

I will predict the classification for this data, I compute the probability of P(Y|overcast, hot, normal, weak) first: 
P(Y|overcast, hot, normal, weak)  
= P(overcast, hot, normal, weak|Y)P(Y) / P(overcast, hot, normal, weak) 
= P(overcast|Y)P(hot|Y)P(normal|Y)P(weak|Y)P(Y) / P(overcast)P(hot)P(normal)P(weak)
= (3/7 * 2/7 * 5/7 * 5/7 * 7/11)  /  (3/11 * 4/11 * 6/11 * 7/11)
= (1050/26411) / (504/14641)
= 0.039756 / 0.034423
= 1.154925

Why the probability(1.154925) greater than 1? 
How can I get right probability in this case by using Naive Bayesian?
 A: There are a few issues here:


*

*You do not actually need to divide by P(overcast, hot, normal, weak) for classification as you just need to see whether P(overcast, hot, normal, weak | Y) P(Y) is bigger or smaller than P(overcast, hot, normal, weak | N) P(N)

*If you do divide then your calculation of P(overcast, hot, normal, weak) should be something like P(overcast, hot, normal, weak | Y) P(Y) + P(overcast, hot, normal, weak | N) P(N) if you want your posterior probabilities to add up to $1$ (this is the direct answer to your question title - neither probability will then exceed $1$)

*You have small sample sizes and in particular all four observed cases of overcast are associated with Y.  That is going to make P(overcast | N) zero in your calculations so, no matter what else the data says about temperature, humidity or windspeed, you will not be able to turn overcast, hot, normal, weak into a classification prediction of N.  This is a feature/bug resulting from a $\text{Beta}(0,0)$ prior, and is probably not a robust approach: among other things it is prone to lead to division by zero with some input data

