  In this article, we prove the existence of at least three positive solutions
for the following nonlocal singular problem \begin{equation*} (P_\la)\left\{
\begin{split} (-\De)^su &= \la\frac{f(u)}{u^q}, \; \; u>0 \;\; \text{in}\;\;
\Om,\\ u &= 0\;\; \text{in}\;\; \mb R^n \setminus \Om \end{split} \right.
\end{equation*} where $(-\De)^s$ denotes the fractional Laplace operator for
$s\in (0,1)$, $n>2s$, $q \in (0,1)$, $\la>0$ and $\Om$ is smooth bounded domain
in $\mb R^n$. Here $f :[0,\infty) \to [0,\infty)$ is a continuous nondecreasing
map satisfying $\lim\limits_{u\to \infty}\frac{f(u)}{u^{q+1}}=0$. We show that
under certain additional assumptions on $f$, $(P_\la)$ possesses at least three
distinct solutions for a certain range of $\la$. We use the method of
sub-supersolutions and a critical point theorem by Amann \cite{amann} to prove
our results. Moreover, we prove a new existence result for a suitable infinite
semipositone nonlocal problem which played a crucial role to obtain our main
result and is of independent interest. \medskip
