Because the probiotics are freeze-dried, they are in an inactive state and stable at room temperature for up to two weeks. The probiotics are only activated once exposed to moisture.
If your probiotic was left out overnight at room temperature with the cap tightly on, your probiotic is completely fine!
If you have the powder probiotic and left it out overnight with the cap off, you should check the powder inside. Especially if it is excessively hot or humid in your area, you should check for your powder's viability by examining the powder for any clumps in the powder. If your powder is still light and fluffy, it should be fine. Any powder that has started clumping has probably been activated by moisture and is no longer viable, and should be thrown out.
If you are using probiotic capsules, they are protected inside the capsule against moisture but please add to cold storage as soon as you can.
Also, for best results against moisture in your product is to leave the silica pack intact during the life of the product and make sure the bottle top is secure.