Probably means that is it more likely to happen. What is likely to be done. For example, “It’s probably going to rain today because the sky looks gloomy.” Stating that most likely going to rain, but you are not guaranteeing that it is going to rain. Possibility means more of a chance type of thing, it goes 50/50. When you use ‘possibly,’ it simply means that you are not sure. For example, “He’s possibly just ignoring you.” Showing the he could be ignoring you, but the person stating this isn’t quite sure. Does this make sense?

Also, probability is a kind of math concept. Something can have a probability between 0 and 1 or between 0% and 100%. So, probability can have a numerical value. Possibility does not.

Possible is used when there is a 50% chance. Probable is used for more than 50% chance. It may rain any day. It is possible that it may rain. If there are large clouds and thunder then rain is probable. If a baby cries it might possibly be hungry or want a toy. If the baby has not eaten for several hours and it cries then it is probably hungry. We should probably lock the car. You should probably take an umbrella with you. "Should probably" makes the sentence sound like a suggestion. I do not want to tell you what to do with your car but I am worried that there could be a theft if you do not lock it. I know carrying an umbrella is an inconvenience but I think it will rain on you if you do not take the umbrella with you. You should probably trust my English phrases because I am a native speaker! Ha ha!

Thank you very much!!!

Ashley nailed it. You should pay attention to her answer.