Difference between conditional and joint probability

Hi,
Can someone explain conceptually what the difference between conditional and joint probabilities is?

Thanks,

The probability that the sidewalk is wet this morning and that it rained last night is 5.4%: joint probability.

The probability that the sidewalk is wet this morning given that it rained last night is 100%: conditional probability.

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Could you please demonstrate the equation of CONDITIONAL PROBABILITY ?
Conditional probability : P(A/B)= P(AB) / P(B)