Question: Suppose the winning combination consists of $7$ digits, each digit randomly ranging from $0$ to $9$. So the probability of $1111111$, $3141592$ and $8174249$ are the same. But $1111111$ seems (to me) far less likely to be the lucky number than $8174249$. Is my intuition simply wrong or is it correct in some sense?

Answer: 
I think the source of the confusion is that human intuition lends itself to some very fallacious reasoning when it comes to probability (and large numbers). The fallacy is this, your intuition groups numbers into two categories: "nice" numbers, and not-so-nice numbers. Suppose we call a "nice number" any number that is just a full sequence of repeated digits. By all means, the probability of getting a nice number is far smaller than the probability of getting a not-so-nice number. Extend this to any number that "stands out" to our perception, and they're still outnumbered by numbers that don't.

The problem with that is, we're not choosing between $2$ "categories", but in fact $10^7$ outcomes.
In canada, lottery tickets are manually drawn and each number cannot be drawn more than once.

For instance, Loto 6/49 (6 numbers, 1 to 49), an "human instution" inprobable number would be 1-2-3-4-5-6 (6 number in a row) and I beleive this is less probable then a more general number like 1-11-20-30-31-45.

Why? Because of the way it's drawn. If the number were drawn all at once by a computer for instance, I wouldnt beleive this. However, it's not the case in this example. Each time a number is drawn, it gets removed from the pot and the pot is scrambled again. Thus, there less numbers in the first 10 digits after each draw, making them less likely to be drawned. 

Call me crazy, but I would never bet my money on a ticket that has 6 numbers in a row.