In a medium bowl, combine the cashews and hot water. Cover and soak the cashews for at least 4 hours, up to overnight. Drain the cashews and discard the soaking water.
Add the drained cashews, cold water, lemon juice, and salt to a high-powered blender. Blend on high speed for 1 minute, until the mixture is completely smooth and creamy.
Transfer the cashew mixture to a clean 16-ounce (455 G) glass jar. One at a time, open the probiotic capsules and pour the powder into the jar, stirring well with a non-metal utensil after each addition to evenly distribute.
Loosely cover the jar with cheesecloth and secure with a rubber band or kitchen twine. Leave the yogurt to ferment in a cool, dark place for at least 12 hours, up to 24 hours. The longer it ferments, the tangier the yogurt will be.
Transfer the yogurt to the refrigerator to cool completely, about 2 hours. Store in the fridge for up to 1 week.