So yes, there is a standard conversion: 1 kJ = 0.24 kCal, or 1 kCal = 4.18 kJ.
But by convention in cycling, kJ is used to measure the work done at the pedals – it is calculated by integrating all the instantaneous power measurements over the time you spent riding. By convention, kCal is used to measure the energy that your body burns during this activity, typically measured from heart rate.
On average – for the average person, at average temperature, air pressure, health etc – people are about 25% efficient, meaning that about 1/4 of the energy that your body puts out [kCal] is reflected in the work done [kJ]. This means that under those conditions, 1 kCal of energy put out gives about 1 kJ of work done at the pedals.
But, if you are less efficient in general [get less work for energy expended], then kCal > kJ. Conversely if you are more efficient. And similarly for different conditions. If one day, your heart rate is high for a particular power output [you are ill, tired or whatever], then energy will be high compared to work done.
So kCal and kJ measures should be approximately equal, but there will be differences in the ratio between people and under different conditions. But, as barrbera says, 593 calories and 1458 kJ is a completely wacky.