Difference between conditional and joint probability

CFA Level I Quant
#1

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

Thanks,

#2

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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#3

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