How to recompute the markov transition matrix given a reduction to the number of states? Clustering from a transistion matrix

Question

I am been puzzled with this one for sometime. Given a transition matrix (as below) for a markov chain of N states; how do we calculate the transition matrix for N-1 states, where we combined stat n1 and n2 (see below).

E.g. Want to go from:

States:          A        B       C      D      E      F 
              A  0.5     0.5      0      0      0      0

              B  0.5     0.1      0.3    0      0.1    0

              C  0       0.1      0.9    0      0      0

              D  0       0        0      0.7    0.3    0

              E  0       0.2      0      0.7    0      0.1

              F  0       0        0      0.5    0      0.5

To :

States:          A        B       C      D+E    F 
              A  0.5     0.5      0      ?      0

              B  0.5     0.1      0      ?      0

              C  0       0.1      0.9    ?      0

             D+E 0       ?        0      ?      ?

              F  0       0        0      ?      0.5

Now I have found I can build this N-1 matrix if I (computationally) simulate the original markov chain (the first transition matrix) and then go back and perform the appropriate state substitution and re-compute the transition matrix.u

My naive instinct is to get the probabilities P(X|D or E) and P(D or E|X) to fill in the ?'s; however, this does not match what you get from the simulation procedure (noted above), at least if you treat

P(X|D or E)= P(X|D)+P(X|E) and P(D or E|X)=P(D|X)+P(E|X) (where X is any of the original states).

Any ideas?