The chance for six ascending balls in a single drawing.

First definition. Let's count a sequence as ascending if the sorted set of drawn balls is ascending. E.g. 18,15,14,19,16 with a powerball of 17 would be counted as ascending.

I found that it was easiest to start with the odd one out and work from there. The powerball can be chosen in 20 ways. If the powerball is 1, then the sequence must start at 1 (1 combination). If it is 2, then the sequence can start with either 1 or 2 (2 combinations), 3 means 3 combinations, 4 means 4 combinations. For 5 and above, there are 5 combinations (the upper part of the range has no similar issue, since the normal balls go all the way to 50). We get a total of 85 combinations.

Now every combination of the 5 normal balls can be permuted in 5! ways, so we have 85 * 5! = 10200 ascending draws.

The total number of possible draws are 50 * 49 * 48 * 47 * 46 * 20 = 5085024000.

So the probability of an ascending draw is 10200 / 5085024000 ~= 2 in a million.