[Edited to reflect @denesp comments]
In asset pricing, the present value of an asset depends on expectations about the future. If you are sure asset A will be worth 100 tomorrow, it is likely to be worth 100/(1+r) today. If you think it might be worth 100 in scenario I or 0 in scenario II with a 1/2 probability each, then its worth [(1/2)*(100) + (1/2)(0)]/(1+r) = 50/(1+r) today.
But, now add the following twist: what if even though the chances of scenarios I and II are 1/2 each, you observe that the asset is worth more than 50/(1+r). Why could this be?
One reason could be that even though the probabilities are 1/2 and 1/2, investors thing they are 3/4 and 1/4 maybe. These would be the "subjective probabilities" according to most direct sources.Investopedia Subjective Probability
Another reason could be that investors know that, for some reason, if scenario I comes round they will be desperate for cash, but if scenario II comes round they will be rich from other income sources anyway. If that's the case then they are more interested in the value of the asset in scenario I than in scenario II. Then they value the asset as being worth, maybe,[(3/4)(100) + (1/4)(0)]/(1+r)=75/(1+r), because the Scenario I payoffs are worth more to them than the Scenario II payoffs.
In any case, if you observe the price to be 75/(1+r) then the numbers 3/4 and 1/4, which look like probabilities, are called the "risk-neutral probabilities". They are "weights" that look like probabilities, that describe two things: investor's subjective assessment of the likelihood of the two scenarios, plus the "importance" they put on different future states of nature, beyond the likelihood of their realization.
These risk neutral probabilities are at the core of the paradigm that economists use to model asset prices .