Generate any three random numbers from any range; sum those numbers; multiply the base number by each of your 3 random numbers in turn and divide by their sum. Result three random numbers that add up to the base number:

Perl> @rands = map{ rand 1000 } 1 .. 3;;
Perl> $t += $_ for @rands;;
Perl> ( $x1, $x2, $x3 ) = map{ 10.33 * $_ / $t } @rands;;
Perl> print "$x1 + $x2 + $x3 = ", $x1 + $x2 + $x3;;

5.13264782081133 + 0.820661299314597 + 4.37669087987407 =  10.33
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