Not that complex ;-), just do:

use strict;

my %a;

$a{"abc"} ++;
print $a{"abc"};
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Two things:

1. In this case you don't need to initilize the hash element, as Perl will initilize it to 0 for you, in a number context.
2. Just in case you do not know, exists is different from defined. If a hash element has value undef, than it exists, although not defined.
   
   This demo would help you to understand:

   use strict;
   
   my %a;
   
   check();
   print "now set abc to undef\n";
   $a{"abc"} = undef;
   check();
   
   sub check {
       print "defined\n" if (defined($a{"abc"}));
       print "exists\n" if (exists($a{"abc"}));
   }
   [download]