I found the code a bit confusing, but I think what is happenning is that you are creating an array that maps a distance from the centre to a record -- but you don't account for the possibility of two records with the same distance.

The approach you probably want to use is to create a reshref for each record, and then sort those by distance. i.e.

while (<LINE>) {
  @fields = split;
  my $record = {
    ra => ...,
    prob => ...,
    dist => ...,
  };
  push @records, $record;
}
sub by_distance { $a->{dist} <=> $b->{dist} }
@records = sort by_distance @records;
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You can then iterate ocver the records, and print them.