The existing kitchen light was taken down, it was always blowing the bulbs. Currently, there's no light fixture up, just a connector type thing. Is this wired correctly? I've attached a photo, the light is operated by 2 different switches, either end of the kitchen. Thank you
When the light was in did the switches work correctly where 1 switch can turn the light off or on? Then the other could turn the light on or off. Wiring is not going to cause a light to blow if the switches work correctly. There may be problems with the main or another load is creating large spikes shorting the life. Here in the US I purchased cases of lamps prior to the outlaw of standard 100w bulbs , some of those old bulbs burn right out because they were not well made but if the switches work correctly there is another problem. Added since op said switches working. If the switches work properly the wiring at this point is not the problem. Especially with 3 way switch setups it is difficult to tell if properly wired, the only thing that could be wrong is the neutral is being switched and or the hot and neutral are swapped at the fixture. Even if this was the case it would not affect bulb life.
Things that do affect bulb life are large voltage spikes and over voltage. I am guessing the reason everything tripped out is that when the filament in the lamp failed it shorted, this failure is not uncommon it has happened to me and I have been called several times because the breaker kept tripping At customer homes, remove bad lamp and everything is good. Could there be something wrong with your fixture? Yes it could have caused the short but that is unlikely. Looking at the wires if no burn marks or bad insulation it was probably the fulfilment in the lamp. Last one thing the fixture can contribute to a shortened life if the center contact is arcing (not a tight contact) this can erode the base of the lamp but I would expect you to notice that and probably hear it but that's the fixture and not the wiring. Hope that helps.