It depends if the bacteria are enterocoated or not. If enterocoated, any time of day. If not, preferably with the food intake, as pH in the stomach gets less acidic and consequently it will affect less to the probiotic viability.
I agree with Monica, but I think if your probiotic is good enough, it should withstand acid/bile stress conditions in the gut, that are what make it probiotic culture.
To my knowledge, the food intake can have both positive and negative impact on the performance of probiotic. The health benefit will depend on the food composition and the subsequent sensibility of the probiotic to it. For example, if the food contains substances that are likely to act as prebiotic, it will definitely enhance the performance of the probiotic culture, hence the health effects.