It's been raining all day. (하루 종일 비가 내리고 있어요.)

I went to work wearing rubber boots and brought an umbrella because it was raining a lot yesterday.

When it is raining, if you wear rubber boots, they are impermeable to rain.

Although this sentence is grammatically correct, it sounds a bit unnatural.
You might try saying: "When it is raining, you should wear rubber boots because they are impermeable to rain." or "When it is raining, I wear rubber boots because they are impermeable to rain."

Many of my coworkers don't work in a rainy day.

It's because accidents are more likely to occur.

Relatively, it's busier on a rainy day.

In English, the word "it's" would not be capitalized unless it was the first word of a sentence.

I went to work wearing rubber boots and bring brought an umbrella because it was raining a lot yesterday.

You must use "brought" in this situation because you made an action in the past.

When it is raining, If if you wear rubber boots, it's they're impermeable to rain.

You do not need to capitalize "if" when it comes after a comma. Also, since "boots" is plural, you need to make your pronoun (they or it) also plural. "They" would represent a plural noun, while "it" would represent a singular noun.

Many coworkers don't work in a on rainy days.

Unless you are talking about a specific day, you should make "day" plural. Also, you use "on" instead of "in" when talking about doing an action on a certain day.

It's because accident probability are many there is a higher probability of accidents occuring on rainy days.

Your sentence did not sound very natural. When talking about probability, use the words "high", "higher", "low", "lower", "great", "greater", "less" or "lesser". There is not a number of probabilities, like you said when using many.

Relatively, It's it's more busy busier in a rainy day on rainy days.

You do not need to capitalize words after commas every time, like you do after question marks or periods. Also, you should use "on" instead of "in" when talking about doing something on a certain day.