Taking a pair of triple hets (Aa Bb Cc) and getting the probability of being homozygous at all three loci is hard to figure out. You could have any combination of homozygous mutant with homozygous normal. After all, AA bb cc, aa BB cc, aa BB CC, etc. are all triple homozygous. However, you probably want to know the probability of being homozygous for all three mutants (aa bb cc).
That is 1/64, and the probability of being triple homozygous normal (AA BB CC) is also 1/64.
The probability of a baby being homozygous for at least one mutant is easy to calculate. The probability is 1 - (3/4 x 3/4 x 3/4) = 1 - 27/64 = 37/64 = 0.578.
The probability of a baby being aa bb but not cc (homozygous aa and homozygous bb) is 1/4 x 1/4 x 3/4 = 3/64.
The probability of a baby being aa cc but not bb (homozygous aa and homozygous cc) is 1/4 x 3/4 x 1/4 = 3/64.
The probability of a baby being bb cc but not aa (homozygous bb and homozygous cc) is 3/4 x 1/4 x 1/4 = 3/64.
So the probability of a baby being homozygous for two mutants (without specifying which two) is 3/64 plus 3/64 plus 3/64 = 9/64 = 0.141. Adding the probability of a triple homozygote gives the probability of getting a baby that is homozygous for at least 2 mutants = 9/64 plus 1/64 = 10/64 = 0.156.
These calculations assume that homozygosity is what matters, as is the case with three recessive mutants. Throwing in one or more dominant or codominant mutants would probably change the starting questions.
Hope this helps.
Statistics is like a bikini. What it reveals is enlightening; what it conceals is vital. 
Paul Hollander