  The vacuum transition probabilities for a
Friedmann-Lema\^itre-Robertson-Walker universe with positive curvature in
Ho\v{r}ava-Lifshitz gravity in the presence of a scalar field potential in the
Wentzel-Kramers-Brillouin approximation are studied. We use a general procedure
to compute such transition probabilities using a Hamiltonian approach to the
Wheeler-DeWitt equation presented in a previous work. We consider two
situations of scalar fields, one in which the scalar field depends on all the
spacetime variables and other in which the scalar field depends only on the
time variable. In both cases analytic expressions for the vacuum transition
probabilities are obtained and the infrared and ultraviolet limits are
discussed for comparison with the result obtained by using general relativity.
For the case in which the scalar field depends on all spacetime variables we
obtain that in the infrared limit it is possible to obtain a similar behavior
as in general relativity, however in the ultraviolet limit the behavior found
is completely opposite. Some few comments about possible phenomenological
implications of our results are given. One of them is a plausible resolution of
the initial singularity. On the other hand for the case in which the scalar
field depends only on the time variable, the behavior coincides with that of
general relativity in both limits, although in the intermediate region the
probability is slightly altered.
