Let's 1st understand what these planets represent on their own?

Sun - Sun represents Soul, Personality, King, Government, Father, Authority, Career, Top Positions, Ego, Self Esteem, Health, Education etc.

Moon - Moon represents Mind, Emotions, Mother, Local Government, Peace of Mind, Home Environment, Water, Milk etc.

Jupiter - It is the most benefic planet and it represents all the auspicious things like Knowledge, Wisdom, Law, Guru, Spirituality, Religion, Philosophy, Literature, Elderly People and Children etc. For a girl, Jupiter also represents Husband.

3 planetary conjunction - Whenever 3 or more planets are conjunct with each other in a house/sign then things related to that house/sign become a kind of life focus for person. It is because of huge accumulation of energy within 30 degrees of sky. It means not only these 3 planets' energy is going into this house/sign but the energy of at least 4 to 6 house/sign is going into this house/sign as these planets will be ruling some houses in chart. So, this house/sign with conjunction becomes almost the most important house in chart. During Career Consultation, I give a huge importance to any such house which has 3 or more planets in it.

House Ruler - Besides these karaka things, Sun, Moon & Jupiter will also rule some houses in your chart and will represent things related to that house. Of course we can't cover conjunctions Ascendant and house wise else it will never be over. So, you have to include things related to the houses at the time of interpreting this conjunction. Also, we need to keep in mind all Yogas and Raj-Yogas which their conjunction would be making to completely understand the conjunction. Here, we can only cover meaning as per karakas.

Meaning of Sun-Moon-Jupiter Conjunction - First of all, it shows someone who is totally knowledge oriented. It is because Soul (Sun) and Mind (Moon) both are connected with knowledge & wisdom (Jupiter). This can show someone as Teacher, Guide or Guru. It shows someone in academic field. It can also show someone's parents in same academic field or someone whose parents are his 1st Guru in life. Basically, it is a planetary position all about knowledge, education and wisdom. They feel confident and they gain authority through their education. Their mind feels at peace as they acquire more and more knowledge. At the same time, Jupiter expands the ego, confidence and emotions. Now, it depends on the dignity of these planets to see if that ego or emotions/mindset will be positive or not. The basic fact that all 3 planets are natural best friends, so it shows that they will cooperate with each other really well. If any of or both the planets are combust then we have to take the combust effect too. 

Who will win the Conjunction? - Moon easily get impacted by other planets. So, Moon here is impacted by Sun & Jupiter. It depends on the dignity of Sun & Jupiter to decide who among them will rule over this conjunction 

Dignity & Strength - 

This conjunction can work best in Aries, Cancer Leo, Sagittarius & Pisces as all planets are in good dignity here.

In other signs, at least 1 planet will be in good dignity, hence results of the conjunction will largely depend on which planet is in better dignity in a sign, planets mutual impact on each other, as discussed above, and the dashas.