  We study the Fredholm determinant of an integral operator associated to the
hard edge Pearcey kernel. This determinant appears in a variety of random
matrix and non-intersecting paths models. By relating the logarithmic
derivatives of the Fredholm determinant to a $3 \times 3$ Riemann-Hilbert
problem, we obtain asymptotics of the determinant, which is also known as the
large gap asymptotics for the corresponding point process.
