The U$.$S$.$ Census Bureau says that the $10$ most common names in the United States are $($in order$)$ Smith, Johnson, Williams, Brown, Jones, Miller, Davis, Garcia, Rodriguez, and Wilson. These names account for $9\mathrm{.}6\%$ of all U$.$S$.$ residents. Out of curiosity, you look at the authors of the textbooks for your current courses. There are $12$ authors in total.

What is the probability that none of the $12$ names of these authors were among the $10$ most common? $($Assume that authors' names are independent and follow the same probability distribution as the names of all residents.$)$ Give your answer to three decimal places.