It is almost never possible to change someone's belief by simply producing a rational argument. I agree with Ninuu's point about it being like religion, however, I don't agree with the idea that one side of the argument is "stupid". It is simply that each side looks "stupid" from the other's PoV because they won't accept your "obvious" rational arguments. That is also partly why people who argue beliefs resort to ad hominem approaches and attack each other personally - you see politicians doing that all the time, for example. The arguments alone have no effect.
The way to change someone's belief is often to appeal emotionally. Create cognitive dissonance repeatedly by showing hard evidence that conflicts with their belief - not opinions. The trouble is in poker that becomes mathematical and peoples' eyes then glaze over. However, showing your winning graph is an excellent idea, also show them all your friends winning graphs. But also talk about all the wonderful things you have done with the money and make it clear that you also have the winnings stable for the longer term - buying a house, or whatever is appropriate in your life stage at the time.
Many people who play the lottery don't get probability and EV, but you could also explain a little how the chances of winning at poker are much better, in ways they can understand.
The thinking behind that:
I'm not familiar with the Canadian lottery but if it is a similar 6/49 format as here, the chances of winning are 1: 14 million ( but adjust to whatever it is - the thinking is the same).
So, for a $1 ticket explain that unless the "pot" is 14 million or more, you are not getting good odds on the bet, and even if the pot is >14 million there is also the possibility you have to share the pot which reduces your value further.
For simplicity's sake with regard to the lower prizes, I'd suggest ignoring that but if asked, point out that it increases the benefit a bit but not hugely. Actually, if you feel inspired to, calculate the total EV of the lottery including shared pots and lower prizes, and then trot it out in terms of the minimum jackpot required for a positive return if challeneged - but better still, show it in physical terms ( see pyramids example below) they will relate to.
However, even with a positive EV there is also the actual probability.
So what I tell people about the lottery is that if my ancestors started buying a weekly ticket at the times the Egyptian pyramids (or stonehenge, a local feature here) were built, and continued down the generations to the present, then on average they might have expected to have won the jackpot once in all that time. But its a coin flip, with a reasonable chance that they wouldn't have won it at all. Most people seem to get that when you put it that way.
And then explain that with Poker on the other hand, you get to set the odds yourself for others to bet as well as to bet on the odds presented, and the odds are much better. And thats the difference between poker and lotteries and casino games.
Although with beliefs, by the time you bring it up with them again a week later, chances are they will have forgotten that you told them. 
So if they still don't get it. Well as they say (nothing personal to anyone, just an expression) don't try to teach a pig to sing. It wastes your time and it annoys the pig..
