Load Factor ($\alpha$) means = $\frac{No.\ of Elements\ needs\ to\ be\ inserted}{Size\ of\ Hash\ Table}$
Well, $\alpha$ will always be less than 1 because if hash table is full there is no point of inserting an element.
Now, suppose there are some elements already in Hash table.
So using above Knowledge of Load Factor $\alpha$, We can say that "There are $(1 - \alpha )$" fraction/part of hash table is empty.
Now the expected number of probs require to insert an element is = equal to = The probability that the element will hit/find the empty place we have available here.
and the probability is = $\frac{1}{(1 - \alpha )}$.
For more information, watch this NPTEL video (from 50:00 minute).
