What are the chances of winning the lottery twice?

John Talbot, Reader of Mathematics at UCL has looked into the odds. Here in the UK, as of January 2014, there have been 1882 lottery draws and 4503 jackpot winners (giving an average of 2.4 winners per draw).

Talbot writes:

'Assuming that:

-Winners consider themselves lucky and so continue to play (twice a week).
-Jackpot winners live for 30 years (from the date of their first win).
-The overall number of players doesn't decrease (and so the average number of winners each week remains at least 2.4).
-The lottery runs for another 20 years.
-Players choose their numbers independently at random (say by using the Lucky Dip option).

The chances that someone wins the lottery twice before 2034 is greater than 60%.' (John Talbot, UCL Twitter)

So why it isn't one in two hundred trillion?

'In each draw the chance of a single ticket winning is around 1 in 14 million. (Actually it's 1 in 13,983,816 = 49×48×47×46×45×44/6!.)

So if you buy a single ticket in each of two draws then your chances of winning the jackpot on both occasions is 1/14,000,000 × 1/14,000,00 which is roughly one in two hundred trillion.'

Talbot offers his calculations here. Mr and Mrs Long have been lucky but Talbot argues that the idea that the chance of this happening is 1 in 200,000,000,000,000 (two hundred trillion) is ridiculous; when, in fact, we should be more surprised if it did not happen at all.