A machine for producing a new experimental electronic component generates defectives from time to time in a random manner. The supervising engineer for a particular machine has noticed that defectives seem to be grouping $($hence appearing in a nonrandom manner$),$ thereby suggesting a malfunction in some part of the machine. One test for nonrandomness is based on the number of runs of defectives and nondefectives $($a run is an unbroken sequence of either defectives or nondefectives$).$ The smaller the number of runs, the greater will be the amount of evidence indicating nonrandomness. $12$ components are drawn from the machine. For example, an arrangement with two runs could be one where the first $10$ components were not defective, and the last $2$ were defective $(N$ N NN NNN NN NDD$).$

When $12$ components are drawn from the machine, what is the probability that the number of runs, $R,$ is less than or equal to $3,$ given that $10$ of the $12$ components are not defective? $($Round your answer to four decimal places.$)$