The odds are not irrelevant at all. In fact they are essential when it comes to separating from false hope and real hope and wishful dreaming.
When the odds are impossible, with chance of a positive outcome at exactly zero, the hope is irrational, at least if you know or should know that it is 0.
When the odds are possible, such as a one billionth chance of winning the lottery, the hope is slim, although rational. If your estimation of the probability is far removed from reality, then also this hope would be irrational. For example, I can buy a lottery ticket, but expect on continuing with that the rest of my life without seeing a profit. I can hope to win, rationally. However, if you go and buy a lottery ticket, and then proceeds to buy a new ferrari and a house as if you'd already won the lottery, then your hope is irrational.
When I at my ripe age enter a marathon trace, I don't hope to win. I can hope to finish in 5 or 6 hours or whatever it is, several hours after teh winners have crossed the goal line. I could hope of being among the top contenders in my age group, or even win the age group. If I hoped to win the whole thing, not only would I be irrational, I'd probably cause severe harm to health trying to compete at a level far beyond abilities.
Likewise, if your project has 3 weeks worth of effort remaining before it is anywhere near done, but the deadline is in 30 minutes, then the hope of making that deadline is irrational, and trying to rush things to make that deadline would probably do more harm than good..