01-Capture the user choice in a variable.
02-Check if it is in the populated array.

##</code><code>##

use strict;
use warnings;
use Tk;
require Tk::BrowseEntry;
my @items = qw(first second third fourth);

my $mw = MainWindow->new();
my $default_choice = "first";
my $dropDown = $mw->BrowseEntry(
   -label=>'items',
   -variable=>\$default_choice,    #capture the user choice or show default
   -browsecmd=>\&doIt
   )->pack();

$dropDown->insert('end', "First");
$dropDown->insert('end',"Second");
$dropDown->insert('end',"Third");
   
$mw->Button(-text=>'exit', -command=>sub{exit;})->pack();
MainLoop;

#check if the array has an element identical to what's been chosen..
sub doIt{
    my $x = -1;
    foreach my $element (@items){
        $x++;
        print $element eq lc($default_choice)? "$default_choice index \$items[$x]\n" : next;
        }
    }

##</code><code>##