list manipulation – the multinomial must receive a machine size number

I need to use multinomial distribution.

In a certain step, by coincidence, the input probability vector is {2.6662875218 * ^ - 903, 6.180318409067 * ^ - 751, 0.5, 6.180318409 * ^ - 751, 0.5}.

When I do

RandomVariate[
 MultinomialDistribution[
  1, {2.6662875218*^-903, 6.180318409067*^-751,  0.5, 
     6.180318409*^-751, 0.5}], 1]

I receive an error message for the values ​​2.6662875218 * ^ – 903 and 6.180318409 * ^ – 751, not being real numbers the size of a machine … When I am run my program on data, the vector of probability number of components is of magnitude of 10 ^ 3.

What is the most effective way to solve this problem?