So, while possibility deals with things that have the potential to be true, probability deals with things that are likely to be true.

In this category, we use must when we have a good reason to believe, or a convincing explanation for strongly considering something to be true. It expresses strong probability. For example, if it was late at night and you knew your friend had not eaten anything all day, you could say, "You must be starving. You haven't eaten anything since breakfast!" While you cannot be certain they are hungry, you have a strong justification for believing that they are.

Should has a slightly different use. It is more a suggestion that something is true in the present or future; though, like must, it cannot be applied without good reason. Another way of understanding it is to think of should as being a reasonable expectation. For example: "I sent John an e-mail with all the information, so he should know what he has to do." In this example, you do not know for certain that John knows what to do, but since you sent him an e-mail explaining things, it is reasonable to expect that he does.

When using must or should to refer to the past, we add have.

We use must have when there is a convincing explanation for strongly believing something to be have been true in the past. For example, imagine your friend is telling you about something that happened to them. They might say, “I fell off my bike last week and was nearly hit by a car.” You might respond: “That’s awful, you must have been so scared!” Taking into consideration the situation being described to you, you can with good reason assert a strong belief that your friend was scared - therefore it is correct to use must have.

When making an informed suggestion about something in the past, we use should have. For example: "They landed in Paris three hours ago, so they should have checked into their hotel by now." Again, considering the circumstances, it is reasonable to expect that they have checked into their hotel, even if you do not know for certain that they have.

When we speak of complete certainty, we are referring to something that we know is definitely true.

Will expresses a conviction that something will happen in the future. In some ways it can be viewed as a certain prediction. For example, you could say with certainty that tomorrow the Sun will rise in the East, and will set in the West. Or, if it is winter and the evenings are dark, you could say with certainty that: "It will be dark by 6 pm."

Will can be contracted by adding 'll to certain pronouns (I, you, she, he, we, it, they, that). For example: "I'll be in hospital for a routine procedure tomorrow."

Shall can be interchanged with will, but is usually only used when we want to express future certainty in a more formal way. Strictly speaking, shall should only be used with first person pronouns (I and we). For example: "I shall attend a dinner party this evening."