If I understand you, perhaps you don't need an array of zeroes; rather, you need a hash. The hash keys will be the values in the other array and the hash values will be the number of times the value exists in the other array:
use strict;
use warnings;
my @other_array = (0,0,0,1,2,2,3,3,3,4);
my %tallies;
$tallies{$_} ++ for @other_array;
print "$_ => $tallies{$_}\n" for sort {$a <=> $b} keys %tallies;
Output:
0 => 3
1 => 1
2 => 2
3 => 3
4 => 1
To answer your specific question more directly, to create an array populated with a bunch of zeroes, you can use the technique in these two examples:
my @zeroes = (0) x 5; # (0,0,0,0,0)
my @zeroes = (0) x @other_array; # A zero for each item in @other_array.
# This works because in scalar context
# an array evaluates to its size.