Simple, assign the random index to a variable and splice using that variable:

for (1..$a) {
        my $foo = rand @thumbs;
        my $randomelement = $thumbs[$foo];
        my $url = "picture_directory/$randomelement";

        print qq(<img src="$url">$url<br>);
        splice(@thumbs, $foo, 1);
}
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Update: hooray for redundancy!

[ ar0n ]