What is meant by risk neutral probabilities?
The name is a misnomer: they’re not probabilities; they’re weights.
It simply means that they’re the weights you need to meet some underlying condition. For example, in a binomial tree for prices (of a stock, say), the weights ensure that the weighted average future value is the present value increased at the risk-free rate.
Note, by the way, that if you forget the formula for the weights, you can determine them easily enough without the formula; if w is the weight for the up price, then:
w × Pup + (1 – w) × Pdown = P0 × (1 + r)
Great explanation even several years after someone can benefit from you Magician 
My pleasure.