Lotto Probabilities

Is the probability of drawing six consecutive lotto numbers, e.g. the first set following, different than the probability of getting six random numbers, e.g. the second set following?
     5, 6, 7, 8, 9, 10          1, 13, 15, 29, 49, 32

They are equal, but many people believe the second set is more likely to be drawn. I guess they believe that because random numbers are more likely to be drawn. Indeed, that is true in aggregate. But to impute that to one combination commits the fallacy of division. Suppose  there are Z possible combinations and N is the number of consecutive combinations. Then the probability of drawing one consecutive combination is (1/N) * (N/Z) = 1/Z. The probability of drawing one non-consecutive combination is (1/(Z-N)) * ((Z-N)/Z) = 1/Z.