Of course there is Hashgacha Pratis during the 3 weeks! There is something very interesting that we find in hilchos Tisha B’av. We sit on the floor, recite kinnos, don’t even greet each other yet surprisingly we omit tachanun; just like we find by the other moadim. Why is this so? The verse in Eichah (1:16) tells us, ‘מועד עלי ‘קרא. From here we see that Tisha Be’av is considered to be a moed and therefore just like with the other moadim we don’t say tachanun We can understand why in the future Tisha B’av will be a moed, but why even now does it already have the status of a moed? The Chasam Sofer explains that since our mourning is coming from hope, therefore, the Bais Hamikdash is still considered alive and it has the status of a moed! And a moed is a time when we come close and we connect with Hashem!