Divide selected value by count(*) - sql-server

Question

I have a Microsoft SQL Server with the following tables:
Projects
BookedHours (with fk_Project = Projects.ID)
Products
ProjectsToProducts (n:m with fk_Projects = Projects.ID and fk_Products = Products.ID)
I now want to select how many hours are booked to which product per month. The problem is, that one project can have multiple products (that's why I need the n:m table).
If I do the following, it will count the hours twice if a project has two products.
SELECT
P.ID AS fk_Product, MONTH(B.Datum) AS Monat, SUM(B.Hours) AS Stunden
FROM
tbl_BookedHours AS B
INNER JOIN
tbl_Projects AS M on B.fk_Project = M.ID
INNER JOIN
tbl_ProjectProduct AS PP ON PP.fk_Project = M.ID
INNER JOIN
tbl_Products AS P ON PP.fk_Product = P.ID
WHERE
YEAR(B.Datum) = 2020
GROUP BY
P.ID, MONTH(B.Datum)
ORDER BY
P.ID, MONTH(B.Datum)
I can get the number of products for each project with this SQL:
SELECT fk_Project, COUNT(*) AS Cnt
FROM tbl_ProjectProduct
GROUP By fk_MainProject
But how can I now divide the hours for each project by its individual factor and add it all up per product and month?
I could do it in my C# program or I could use a cursor and iterate through all projects, but I think there should be an more elegant way.
Edit with sample data:
|----------------| |----------------| |------------------------------|
| tbl_Projects | | tbl_Products | | tbl_ProjectProduct |
|----------------| |----------------| |------------------------------|
| ID | Name | | ID | Name | | ID | fk_Project | fk_Product |
|----+-----------| |----+-----------| |------------------------------|
| 1 | Project 1 | | 1 | Product 1 | | 1 | 1 | 1 |
| 2 | Project 2 | | 2 | Product 2 | | 2 | 1 | 2 |
| 3 | Project 3 | | 3 | Product 3 | | 3 | 2 | 1 |
| 4 | Project 4 | | 4 | Product 4 | | 4 | 3 | 3 |
|----------------| |----------------| | 5 | 4 | 1 |
| 6 | 4 | 2 |
| 7 | 4 | 4 |
|------------------------------|
|--------------------------------------|
| tbl_BookedHours |
|--------------------------------------|
| ID | fk_Project | Hours | Date |
|--------------------------------------|
| 1 | 1 | 10 | 2020-01-15 |
| 2 | 1 | 20 | 2020-01-20 |
| 3 | 2 | 10 | 2020-01-15 |
| 4 | 3 | 30 | 2020-01-18 |
| 5 | 2 | 20 | 2020-01-20 |
| 6 | 4 | 30 | 2020-01-25 |
| 7 | 1 | 10 | 2020-02-15 |
| 8 | 1 | 20 | 2020-02-20 |
| 9 | 2 | 10 | 2020-02-15 |
| 10 | 3 | 30 | 2020-03-18 |
| 11 | 2 | 20 | 2020-03-20 |
| 12 | 4 | 30 | 2020-03-25 |
|--------------------------------------|
The Result should be:
|----------------------------|
| fk_Product | Month | Hours |
|----------------------------|
| 1 | 1 | 55 |
| 2 | 1 | 25 |
| 3 | 1 | 30 |
| 4 | 1 | 10 |
| 1 | 2 | 25 |
| 2 | 2 | 15 |
| 1 | 3 | 30 |
| 2 | 3 | 10 |
| 3 | 3 | 30 |
| 4 | 3 | 10 |
|----------------------------|
For example booking Nr. 1 has to be divided by 2 (because Project 1 has two products) and one half of amount added to Product 1 and the other to Product 2 (Both in January). Booking Nr. 4 should not be divided, because Project 3 only has one product. Booking Numer 12 for example has to be divided by 3.
So that in total the Hours in the end add up to the same total.
I hope it's clearer now.
*** EDIT 2***
DECLARE #tbl_Projects TABLE (ID INT, [Name] VARCHAR(MAX))
INSERT INTO #tbl_Projects VALUES
(1,'Project 1'),
(2,'Project 2'),
(3,'Project 3'),
(4,'Project 4')
DECLARE #tbl_Products TABLE (ID INT, [Name] VARCHAR(MAX))
INSERT INTO #tbl_Products VALUES
(1,'Product 1'),
(2,'Product 2'),
(3,'Product 3'),
(4,'Product 4')
DECLARE #tbl_ProjectProduct TABLE (ID INT, fk_Project int, fk_Product int)
INSERT INTO #tbl_ProjectProduct VALUES
(1,1,1),
(2,1,2),
(3,2,1),
(4,3,3),
(5,4,1),
(6,4,2),
(7,4,4)
DECLARE #tbl_BookedHours TABLE (ID INT, fk_Project int, Hours int, [Date] Date)
INSERT INTO #tbl_BookedHours VALUES
(1,1,10,'2020-01-15'),
(2,1,20,'2020-01-20'),
(3,2,10,'2020-01-15'),
(4,3,30,'2020-01-18'),
(5,2,20,'2020-01-20'),
(6,4,30,'2020-01-25'),
(7,1,10,'2020-02-15'),
(8,1,20,'2020-02-20'),
(9,2,10,'2020-02-15'),
(10,3,30,'2020-03-18'),
(11,2,20,'2020-03-20'),
(12,4,30,'2020-03-25')
SELECT P.ID AS fk_Product, MONTH(B.Date) AS Month, SUM(B.Hours) AS SumHours
FROM #tbl_BookedHours AS B INNER JOIN #tbl_Projects AS M on B.fk_Project = M.ID
INNER JOIN #tbl_ProjectProduct AS PP ON PP.fk_Project = M.ID
INNER JOIN #tbl_Products AS P ON PP.fk_Product = P.ID
GROUP BY P.ID,MONTH(B.Date)
ORDER BY P.ID, MONTH(B.Date)
This gives me the wrong result, because it Counts the hours for both products:
| fk_Product | Month | SumHours |
|-------------------------------|
| 1 | 1 | 90 |
| 1 | 2 | 40 |
| 1 | 3 | 50 |
| 2 | 1 | 60 |
| 2 | 2 | 30 |
| 2 | 3 | 30 |
| 3 | 1 | 30 |
| 3 | 3 | 30 |
| 4 | 1 | 30 |
| 4 | 3 | 30 |
|-------------------------------|

Answer 1

Consider the following query. I modified your table variables to temp tables so it was easier to debug.
;WITH CTE AS
(
SELECT fk_Project, count(fk_Product) CNT
FROM #tbl_ProjectProduct
GROUP BY fk_Project
)
,CTE2 AS
(
SELECT t1.Date, t2.fk_Project, Hours/CNT NewHours
FROM #tbl_BookedHours t1
INNER JOIN CTE t2 on t1.fk_Project = t2.fk_Project
)
SELECT t4.ID fk_Product, MONTH(date) MN, SUM(NewHours) HRS
FROM CTE2 t1
INNER JOIN #tbl_Projects t2 on t1.fk_Project = t2.id
INNER JOIN #tbl_ProjectProduct t3 on t3.fk_Project = t2.ID
INNER JOIN #tbl_Products t4 on t4.ID = t3.fk_Product
GROUP BY t4.ID,MONTH(date)