You are trying to keep the total sum of all occurrences in $features[$oligos+1] (accessing the n+1th element ) with $oligos being some integer, a global variable from out of nowhere.

Note: this part of the array @features has never been initialized as 0. It works anyway in perl, because ($undef_variable)++ == 1 plus a warning (if warnings are on). Note2: The code contains some important variables defined in global scope, therefore one needs to guess what they are meant to do.

$features[$x] /= $features[$oligos+1]; 
<=> $features[$x] = $features[$x] / $features[$oligos+1];

Now, the only way to get a division by zero is that $features[$oligos+1] == 0, which again means if ( exists( $x_mers{substr($sequence, $x, $mer)} ) ) was never True.

If this part of the code is supposed to find your kmers in 'their' kmers $x_mers and further assuming that this is the correct way of pattern matching, that would simply mean that your $sequence does not contain any of the n_mers in $x_mers and the code does not protect against this case.

#-------------------------------------------------------------------------------
# Purpose   : Builds a feature-vector for each sequence. The features are  
#             oligomer frequencies.
# Usage     : process_sequence($string, $number, *filehandle)

# Look at the required arguments, I guess you should have a $number instead


# Arguments : sequence (string), prefix (number), output (filehandle) Not sure what is meant by prefix
# Returns   : Nothing, prints.
# Globals   : Uses the global variables of the build_tetramer_hash (or pentamer) 
#             subroutines
## global %x_mers (a catalogue of some or all k-mers, with the rank of the k-mers among all k-mers?),
## $oligos (possibly the total number of all kmers in %x_mers, not needed), $mer, this is actually a rather bad idea (possibly x_mers is a huge hash)  

#*******************
sub process_sequence {
    my $sequence = uc($_[0]);
    my $prefix = shift; # The the SVM "classifier"
    my $OUT = shift;    # Filehandle
    my $mer = shift; # mer should be a parameter of the fuction
    ## 
    my $total = 0; # total number of found kmers for normalization
    my $n_oligos = scalar(keys %x_mers) ;
    # The vector of SVM features. Initially every element is zero

    my @features = (0) x $n_oligos; # does the same as the foreach

    my $iterations = length($sequence)-$mer-1;

    # just another example of non-defensive programming: what guarantees that 
    # length ($sequence) > $mer-1, what happens if iterations is negative?!?

    die "input sequence must be longer than $mer+1" unless $iterations > 0; # you could argue that the function should simply return silently in this case

    # Counts the number of occurences of each x-mer in the sequence
    # this is probably fine if the sequence is short in comparison to the
    # kmer catalogue, however there should be more efficent ways to count
    # k-mers in perl in general
    foreach my $x (0..$iterations) {
        if ( exists( $x_mers{substr($sequence, $x, $mer)} ) ) {
            $features[$x_mers{substr($sequence, $x, $mer)}]++;
           $total++;
        }
    }
    # Calculates and prints the frequencies for each oligomer
    warn "None of the $mer mers in the input sequence was found in the kmer catalogue, printing all NA frequencies" 
       if ($total < 1);

    print $OUT $prefix, "\t";
    foreach my $x (0..$n_oligos-1) { # note the -1 .. because scalar gives the number entries
        print $OUT "", ($x+1), ':', ($total)? ($features[$x]/$total):'NA', "\t"; # protects against division by zero,  possibly this output should not be used, or print 'NA' or 'inf'
    }
    print $OUT "\n";    
}