Please tell me how I can calculate "conditional mutual information".
Please provide simple examples (with values) to illustrate your
explanation. Please provide any links that explains this with other
examples. (I have already visited a number of sites which tells me the
formula, but does not provide any examples I can follow with)

MI(X;Y|Z)=H(XYZ)-H(XZ)-H(YZ)+H(Z)

This is the formula to calculate conditional mutual information.

Explanation of the formula:
Here I am calculating mutual information between X and Y when Z is
given (MI(X;Y|Z)). H is the entropy.

Conditional mutual information is mutual information between two
variables when the value of theird variable is known.

Example :
Let Z=X XOR Y and values of X & Y are independent.

MI(X;Y)=0
As X & Y are independent MI is 0. In other words knowing X does not
provide any information about Y (vice versa).

MI(X;Y|Z)=finite value depending upon the the distribution of X & Y

Here MI is a finite values. The reason is When we already have the
knowledge of Z, knowing value of X provides complete information about
the value of Y

Concept of conitional mutual information is easier to follow if you
know the concept of conditional entropy. Visit wikipedia or any other
site for this information. If you need I can provide equations for the
particular problem you are interested with proper explanation.

Hope this helps :)