How are new probabilities computed when simulating measurement on a set of qubits? Suppose I have a set of 3 qubits and I have the probabilities for their distribution. This could be arbitrarily entangled or pure:


|000> -> a 
|001> -> b
|010> -> c
|011> -> d
|100> -> e
|101> -> f
|110> -> g
|111> -> h


With it holding that a^2 + b^2 ... h^2 = 1.

a) Now suppose I wanted to measure the third qubit. Would it be valid to generally take the probability of the measurement being 0 as a^2 + c^2 + e^2 + g^2?

b) Assume I had measured the third qubit as 0. How would I construct a new probability distribution across my remaining 2 qubits:


|00> -> w 
|01> -> x
|10> -> y
|11> -> z


Where w, x, y and z are computed from a, b ... h

Thank you in advance for any guidance you can give me!
Let 
$$P(0) = |a|^2 + |c|^2 + |e|^3 + |g|^2.$$
This is the probability of observing $0$. 

Then
\begin{eqnarray*}
w &amp;=&amp; a \big/ \sqrt{P(0)}, \\
x &amp;=&amp; c \big/ \sqrt{P(0)}, \\
y &amp;=&amp; e \big/ \sqrt{P(0)}, \\
z &amp;=&amp; g \big/ \sqrt{P(0)}.
\end{eqnarray*}