Ratios of isospin amplitudes in hadron decays are a useful probe of the interplay between weak and strong interactions and allow searches for physics beyond the standard model. We present the first results on isospin amplitudes in
b
-baryon decays, using data corresponding to an integrated luminosity of
8.5
 
 
fb
−
1
, collected with the LHCb detector in
p
p
collisions at center of mass energies of 7, 8, and 13 TeV. The isospin amplitude ratio
|
A
1
(
Λ
0
b
→
J
/
ψ
Σ
0
)
/
A
0
(
Λ
0
b
→
J
/
ψ
Λ
)
|
, where the subscript on
A
indicates the final-state isospin, is measured to be less than
1
/
21.8
at 95% confidence level. The Cabibbo suppressed
Ξ
0
b
→
J
/
ψ
Λ
decay is observed for the first time, allowing for the measurement
|
A
0
(
Ξ
0
b
→
J
/
ψ
Λ
)
/
A
1
/
2
(
Ξ
0
b
→
J
/
ψ
Ξ
0
)
|
=
0.37
±
0.06
±
0.02
, where the uncertainties are statistical and systematic, respectively.